Prior to his death, Hoster Tully was the Lord of Riverrun, the Lord Paramount of the Trident and the head of House Tully, one of the Great Houses of Westeros. He was the father of Edmure, Catelyn and Lysa and the brother of Brynden. He ruled over the Riverlands from the castle of Riverrun.
Hoster was the head of House Tully and the Lord Paramount of the Riverlands. The Riverlands are one of the constituent regions of the Seven Kingdoms and House Tully is one of the Great Houses of the realm. House Tully rules the region from their seat at Riverrun and Hoster also holds the title Lord of Riverrun.
Hoster married Lady Minisa of House Whent. They have three children, two daughters Catelyn and Lysa and a son, Edmure. Only three of the six children she bore survived. She died shortly after bearing the last which died with her. Hoster brokered a marriage alliance with the Lords Paramount of the North House Stark, betrothing his eldest daughter Catelyn to their heir Brandon Stark
The Mad King Aerys II Targaryen had Brandon executed triggering a rebellion against him. Hoster joined House Stark, House Baratheon and House Arryn in opposing the Mad King. Catelyn married Brandon's brother Eddard Stark and Hoster arranged for Lysa to marry Lord Jon Arryn to solidify the alliance. They won the war and installed Robert Baratheon as the King on the Iron Throne.
In recent years Hoster had become old and frail, losing a great deal of weight. By the beginning of the War of the Five Kings, Hoster had been bedridden for a considerable amount of time from a prolonged illness, and only semi-coherent. His son and heir Edmure took over the day-to-day rule of Riverrun, and Hoster's other duties as overlord of the Riverlands.
Lord Hoster finally passed away shortly after the Battle of the Blackwater. Hoster's brother Brynden, son Edmure, daughter Catelyn, and grandson Robb Stark are present for his funeral at Riverrun. As per Tully funeral tradition, his body is set adrift on the Red Fork of the Trident River in a funeral boat, and then set on fire by a flaming arrow - so that his ashes will return to the river which sustains their lands. Brynden tells Catelyn that he and Hoster managed to make peace before his death. Hoster told Brynden to stop calling himself "The Blackfish" as it is an old joke and it wasn't very funny to begin with. Following Hoster's death, his son Edmure inherits his titles and lands, and officially becomes the new head of House Tully.
Lord of Riverrun and Lord Paramount of the Riverlands, Lord Hoster passed away during the war. He was especially close to his daughter Catelyn, who would watch from the castle's windows awaiting his return whenever he traveled. A skilled strategist in his heyday, he arranged for his daughters Catelyn and Lysa to marry Ned Stark and Jon Arryn during Robert's Rebellion, thus solidifying his family's power when Robert Baratheon took the throne.