At the beginning of Game of Thrones, we learn that Eddard Stark and Robert Baratheon share a special bond, as they both grew up together under the protection and guidance of Jon Arryn, of the Vale. Jon made his well-protected seat in the Eyrie, high up in the mountains. Despite his advanced age, he took Lysa Tully, Catelyn Tully Stark's sister, as his wife, making he and Eddard brothers-in-law. Early on, we learn that Jon, formerly King Robert's chief advisor, has died - potentially of sinister causes - which is a large motivating factor for Eddard accepting the position of Hand to the King.
Surviving Jon are his wife Lysa as well and his only son, Robin (called Robert in the books). Despite the powerful seat, Robin is a weak, sickly boy, who suffers from seizures and is coddled and spoiled by his overbearing mother.