When we meet Jon Arryn, he is a corpse, having been murdered right before the events of the series. The viewers find out that Jon Arryn was the Lord of the Eyrie and the Hand of the King. He had other titles such as the Defender of the Vale and the Warden of the East.
Jon Arryn was a member of the Arryn line, which was brought together with the Stark line through marriage. Therefore, Arya and Sansa were Jon Arryn’s nieces by marriage. During his life, Jon Arryn mentored and fostered Eddard Stark, so when the Mad King turned against Eddard, Jon Arryn revolted. He allied with the House of Tully, the House of Baratheon, and the House of Stark before going to war.
In his old age, Jon Arryn then married Lysa Tully, a young woman, to cement this alliance. After the Mad King was overthrown Robert came into power, but he did not do much except for eat, drink, and have sex. As the Hand of the King, Jon Arryn was the true man to rule the Seven Kingdoms at this time.
When Jon Arryn died, he was trying to figure out if Queen Cersei’s children were legitimate. He discovered that the children were not biologically Robert’s and died with this knowledge. Jon Arryn died and his last words to Robert were ‘The seed is strong.’ This refers to the fact that all of Robert’s children look like him while Joffrey and the others look like their true parents – Lannisters.
When the Game of Thrones series begins, Jon Arryn is dead, and his corpse is laid out in the Red Keep. Over his dead body, Cersei and Jamie talk about how Jon Arryn did not discover their incestuous relationship. He did, however, get very close, which says a lot about Jon Arryn’s ability to seek out information and dig into other’s relationships.
Later in Winterfell Eddard Stark gets news of Jon Arryn’s death and he is devastated. One can see here that Jon Arryn was beloved by many by this reaction to his death. Robert asks Eddard to take on Jon Arryn’s former role as Hand of the King. Eddard then begins to discover the same secrets that led to Arryn’s death.
Jon Arryn left behind a wife and son, Lysa and Robin. Robin is only a child, leaving the actual ruling of the Eyrie to Lysa Arryn. Lysa is Catelyn Stark’s younger sister.