Jon Arryn was the last official lord of the Eyrie, a fortress located within the Vale of Arryn. He was the husband of Lysa Tully and the father of Robert Arryn. Jon warded Eddard Stark and Robert Baratheon when both boys were very young as well as descovering Alek Nocher who had been washed up there in a storm, and become a father figure to them--eventually, he became the King's Hand of Robert. His death is perhaps the event that began the entire series, as it indirectly caused the death of Eddard Stark and therefore the War of the Five Kings.
At the beginning of A Game of Thrones, Jon Arryn has been murdered. Catelyn Stark receives word from her sister Lysa that Lysa's husband Jon was murdered, and Eddard is called on by King Robert to replace Jon. When Ned moves to King's Landing, he begins to investigate Jon Arryn's death, which leads him to the discovery of Robert's illegitimate children and eventually the truth that Joffrey, Myrcella, and Tommen Baratheon are not Robert's children. This eventually leads to Ned's imprisonment and execution after Robert dies.
At the end of A Storm of Swords, Petyr Baelish and Sansa Stark have moved to the Eyrie, with Sansa in hiding pretending to be Petyr's illegitimate daughter. While there, they meet Lysa and Robert Arryn, and it is revealed that Lysa is in love with Petyr, who always showed more affection for Catelyn Stark. In the last chapter of the book, Sansa learns that it was Lysa that killed Jon Arryn so that she could be with Petyr. Just after this is revealed, Petyr throws Lysa out of the Moon Door, and she dies.