Jaqen H'ghar is a mysterious man - introducing himself as a Lorathi criminal - who was arrested and put in the dungeons of King's Landing, before being recruited by Yoren to join the Night's Watch. He is in Yoren's party as the latter smuggles Arya Stark out of King's Landing. He travels with them to the lands south of Harrenhal, where they are captured by Lannister forces.
In reality, "Jaqen H'ghar" is just an assumed identity of one of the Faceless Men of Braavos, a feared order of mysterious assassins with the ability to change their appearance at will. After the Jaqen persona is of no more use to him, the Faceless Man shapeshifts into a new appearance.
Jaqen is surprisingly calm in the face of danger, yet courteous. He uses an odd speech pattern in which he refers to both himself and others using the third person indefinite, e.g. saying "a man thanks a girl" when he is directly addressing Arya and expressing his own thanks.
Jaqen is a criminal from the Free Cities, arrested by the City Watch and thrown into the dungeons of the Red Keep in King's Landing. When looking for fresh recruits for the Night's Watch, Yoren was given permission by Lord Eddard Stark, Hand of the King to go through the dungeons and take any criminals who would swear to take the black. He chose H'ghar as a potential candidate, as well as two other murderers Biter and Rorge from the black cells, where the worst criminals are kept.
Jaqen H'ghar is in the party led by Yoren that leaves King's Landing for the Wall, along with Hot Pie, Lommy Greenhands, Gendry, and Arya Stark who is being smuggled out to be returned to Winterfell. Because Yoren is traveling so far with so few men, the worst three are kept in a locked barred cell on the back of a wagon.
Jaqen calls over "Arry" (who is actually Arya Stark). He asks her to fill a tankard with water and tells her that he has not drunk for a day and a night, always referring to himself as “a man” and her as “a boy”. Rorge, one of the other prisoners, rattles the cage and threatens Arya. Jaqen asks Arya for forgiveness and tells her that he has not chosen his companions. He confirms her identity as Arry and introduces himself, saying that he comes from Lorath. Rorge demands beer and insults Arya. She says that he should have asked nicely, drops all but one of her sticks and uses it to hit his hand. He recoils and then tries to grab her through the cage. Biter moves up behind Rorge and hisses as Rorge threatens Arya again. Jaqen smiles and tells Arya that she has more courage than sense as she backs away.
The group is resting in a barn when they are roused to arms by Yoren and told they are being attacked. As they rush outside one man trips and drops his torch, setting a fire near the prisoner wagon. They are met by Ser Amory Lorch and a force of men loyal to House Lannister. Lorch points out the Gold Cloaks with him and says that they have come for Gendry, a royal bastard. Lorch orders Yoren and the recruits to drop their weapons. Yoren remains defiant and Lorch orders him shot.
Seeing their leader killed, Gendry and many of the other recruits join the fight. Arya is distracted by Jaqen calling for help as the flames lick the bars of his cage. She hands him an axe before rushing to join the fray. Gendry is overwhelmed and knocked down. As Arya runs round a corner she is knocked over and taken prisoner along with the other survivors. Jaqen does not fight against the Lannister men, though he's surprised that Arya helped him.
The prisoners are taken to Harrenhal, one being picked each day by Ser Gregor Clegane to be tortured and killed under the supervision of a man called the Tickler. Lord Tywin Lannister arrives and ends the pointless brutality, choosing Arya as his cupbearer. After being told to fetch water by Tywin Lannister, Arya meets Jaqen again; however, he is dressed in a Lannister uniform. She accuses him of being "one of them now", but he counters her, questioning for whom she is fetching water.
Jaqen says he always knew she was a girl, but she was entitled to her secret. He then informs her of the debt he, Rorge, and Biter owe her. Because she saved three lives, she has taken three lives from the Red God. He says that they must be given back and that she is to name three people who will be killed to repay the debt. Arya names the torturer known as The Tickler. The Tickler is found dead in the courtyard, under the windows of a raised walkway. Arya goes to the body and looks up to see Jaqen staring down. He touches his cheek with one finger, indicating that the first death has been repaid.
Jaqen is approached by a panicked Arya, who desperately requests her second death: Ser Amory Lorch. He had become suspicious of her intent while ferreting Lannister documents. Jaqen bristles at her insistence on urgency. Arya explains the situation and he reluctantly obliges, assassinating Ser Amory with a dart dipped in wolfsbane to the neck seconds before he reaches Tywin Lannister.
The assassination triggers the suspicion of Tywin, and he orders the interrogation and execution of dozens of his own men in order to solve it, but does not uncover Jaqen. Tywin leaves Harrenhal while Jaqen is on patrol; Arya is frustrated as she had decided to make him her last name. Instead she asks Jaqen to aid her and her friends in escaping but he refuses, as it is outside of their arrangement. She asks if she can name anyone and Jaqen swears an oath that who ever she names he will kill. To his horror, Arya says his own name and tells him to go kill himself. At Jaqen's plea, she agrees to revoke his name only if he will help her. He reluctantly tells her to assemble her friends at the courtyard gate at midnight. At midnight there is no sign of Jaqen but Arya follows his instructions anyways, only to find out that Jaqen has killed all of the guards on the gate and pinned them in place with spears to avoid arousing suspicion. They are able to walk through the gate unnoticed
Having left Harrenhal, Arya, Gendry and Hot Pie see Jaqen on top of a cliff. Arya approaches him and he offers to take her with him to Braavos to join the Faceless Men. Though she wants to, Arya declines saying she must find her brother, mother and sister. Jaqen gives her a coin and tells her that if she decides to go to Braavos she must show the coin to a Braavosi and say the words "Valar Morghulis". He tells her to say the words and then announces that Jaqen H'ghar is dead. He turns his face away from Arya and when he turns back his face has changed. "Jaqen" then says "Farewell, Arya Stark" and walks away, seeming to have known her true identity all along.
Arya comes across a ship preparing to leave while travelling on her horse. Arya first asks the captain to take her to the Wall, her intent being to meet up with her brother, Jon Snow. When the captain, Ternesio Terys, tells her that he is in fact going to the Free City of Braavos, his home, Arya shows him the iron coin which Jaqen H'ghar gave her. As Terys looks in awe, she tells him "valar morghulis". He promptly nods his head and replies "valar dohaeris", offering her a cabin aboard the Titan's Daughter. Arya is then shown sailing away on the ship, headed to Braavos, to find Jaqen H'ghar.
At Braavos, after being dropped at the House of Black and White, Arya Stark calls to the door of the ancient building. An old man answers her call and she asks for Jaqen H'ghar, only to be told that there is no one by that name inside. Some time later, Arya is saved by the same Faceless Man and follows him. Before the gates of the House of Black and White, the man assumes the visage Arya had known him as —that of Jaqen H'ghar. However, he insists he's not Jaqen H'ghar, but "no one", as all Faceless Men are, and he tells Arya she must learn to be "no one" as well.
A few days later, Jaqen helps a man commit suicide while Arya watches and sweeps the floor. When she comes to him and tells him that she no longer wants to sweep the floor because she wants to train, he tells her that she is training: to serve, as all Faceless Men must.
Jaqen later interrupts the Waif as she plays the 'game of faces' with Arya, claiming that she is not ready. When he sees all her things in her room, including her sword Needle, he hints to her that she must dispose of all ties to her former life as Arya Stark in order to continue her training to be "no one". After Arya disposes of her belongings, Jaqen takes her deeper into the House of Black and White where she is to help the Waif clean the bodies of those who have taken their lives in the House.
Later, when Arya is asleep, Jaqen H'ghar comes to test Arya again. This time, when he asks Arya who she is, Arya tells him how she came to join the Faceless Men, trying to slip in a few lies into the story. However, Jaqen is able to tell when Arya is lying and hits her with a switch whenever she does. Before he leaves, he tells her that she is lying not only to him, but to herself as well.
When, eventually, Arya proves herself, Jaqen brings her to the Hall of Faces, a great underground chamber that houses thousands of faces. All the faces had been taken from the corpses that the acolytes wash in the temple. The Faceless Man then asks Arya if she is ready to give up who she is to become "no one". After a moment of silence, he then states that she is not ready to become "no one", but that she is ready to become "someone else".
Arya assumes the identity of Lanna, a clam-seller, and shows Jaqen H'ghar she can convincingly become a different person, developing an elaborate and very believable backstory. The Faceless Man sends her, as Lanna, to the harbour where she observes someone referred to as "the thin man" refuse a contract to insure a man's boat, leaving the man in desperate circumstances. Jaqen explains the thin man's business is a sort of gamble yet he does not honour his agreements; when a ship captain dies at sea, he is supposed to make good on his promise and pay the family, but he often doesn't. Jaqen instructs her to kill him, and hands her a "gift" for the thin man —a vial of poison.
The next day, Arya returns to the House of Black and White empty-handed, having abandoned her first mission for the Faceless Men. When Jaqen H'ghar asks what happened, she lies to him and says that the Thin Man simply wasn't hungry today and didn't order any over her oysters. Jaqen quips that perhaps this is why he is a "thin man", and Arya promises that she will follow through on the assassination tomorrow. She departs, and while Jaqen seems to suspect that she was lying, he makes no outward reaction to it. Arya will have a lot of work to do soon.
After killing Meryn Trant, Arya returns to the House of Black and White and returns the face that she used to hide her identity. However, Jaqen H'ghar and the Waif appear and say that Meryn's life was not hers to take, and that a debt must be paid. The Waif grabs Arya as Jaqen pulls out a vial, presumably containing some kind of poison. He however drinks the poison himself and collapses, with Arya screaming for him to stay alive. Arya states that he was her friend, and hears Jaqen's voice behind her say 'he was no one'. She turns around to see that the Waif now has Jaqen's face, and Arya asks who the person on the floor with Jaqen's face is. Jaqen, in the Waif's body, says that he is no one, as Arya begins to remove multiple faces off the person on the floor, until she sees her own face. She then begins to lose her sight, as her eyes turn white and screams for help.
After being hit by the Waif, Arya tries to strike back with her rod, only to have it caught in mid-air by Jaqen H'ghar, who seemingly replaced the Waif. He promises that if she says her name, he would provide her shelter, clothes and have her eyesight restored. However, Arya resisted the temptations and said that she has no name. Satisfied, he tells Arya to follow him, and that she is a beggar no more.
Back at the House of Black and White, Jaqen observes the Waif fighting with Arya and is pleased to see Arya successfully defend herself while still blind. He offers to give Arya her sight back if she says her name, and as before, she says "A girl has no name." He calls her to come to him at the central fountain, fills a cup from the pool, and hands it to her. Arya hesitates for a moment, knowing that the water is poisoned and meant for those seeking a quick and painless death. Jaqen reminds her that as someone with no identity at all, she should be completely void of fears. Arya calmly drinks from the cup, and her sight is restored.
Jaqen gives Arya the task of assassinating Lady Crane, an actress in a troupe, and implies that she will be marked for death if she is not successful. Arya reconnoiters her target at a play caricaturing the War of the Five Kings, and notes that Lady Crane is the only one who drinks from a certain bottle of rum. The two agree that poisoning the rum will be the method of assassination, and Arya proceeds to poison Lady Crane's rum at another showing of the play. When Arya prevents the assassination from occurring, Jaqen gives the Waif permission to hunt down Arya.
While pacing the atrium of the House of Black and White, Jaqen notices blood on the ground. He follows the trail to the Hall of Faces, where the trail stops at a new face on the wall, that of the Waif. Arya sneaks up behind him and points Needle at him. Jaqen does not offer resistance, and even walks into the sword's point. Though she rejects the tenets of the Faceless Men and reclaims her identity, Jaqen is pleased with her conduct, and allows her to leave.
"Recruited" from the black cells of King's Landing into the Night's Watch, Jaqen H'ghar and two companions were saved after the Lannisters attacked their party. To repay the three lives thus stolen from the Red God, Jaqen offered Arya three kills and ultimately helped her escape from Harrenhal. He provided her with an iron coin to ensure her safe passage to Braavos if she ever desired to learn the deadly arts of his order, the Faceless Men. Arya used the coin to find him at the House of Black and White, and he guided her through rigorous training. Despite his protégé's disobedience, Jaqen had confidence that she could become No One. He accepted her fully after the girl killed the Waif, but Arya was unwilling to renounce her identity as a Stark.