GILLY'S DISCOVERY ABOUT RHAEGAR AND LYANNA
In "Eastwatch," Gilly finds a record at the Citadel that Prince Rhaegar married Lyanna Stark in a secret ceremony in Dorne. High Septon Maynard recorded the annulment of Rhaegar's marriage to Elia Martell. We also recall that Oberyn Martell (Pedro Pascal), Elia's brother, told Tyrion Lannister (Peter Dinklage) in season four that he despised Rhaegar for leaving his sister for another woman. This completely contradicts the story that Lyanna was abducted, raped, and murdered by Rhaegar, and the Citadel kept legal proof.
Lyanna and Rhaegar were in fact legally married; their romance began at that fateful tournament at Harrenhal and blossomed since. Rhaegar even left his wife Elia for his new bride, who in turn willingly ended her betrothal to Robert Baratheon, which Robert blamed entirely on Rhaegar as her 'abductor,' likely unable to face the thought that Lyanna didn't reciprocate his feelings towards her, despite being promised to each other. Meanwhile, having more than one wife isn't unusual behavior for a Targaryen. The Targaryen family have a history of polygamy dating back to Aegon the Conqueror, who was married to both his sisters simultaneously. But that isn't the case with Rhaegar. He left Elia - a marriage arranged by the Mad King - for Lyanna, whom he fell in love with and she apparently reciprocated that love.
We also know from Bran's flashback to the Tower of Joy in season six that at the end of Robert's Rebellion, his father Ned, Howland Reed, and four Stark knights went to Dorne to search for Lyanna and found Ser Arthur Dayne AKA The Sword of the Morning, Ser Oswell Whent, and Ser Gerald Hightower, who was Lord Commander of the Kingsguard. Ned even questioned why three of the most famous knights of this era were mysteriously guarding Lyanna Stark in the Tower instead of fighting alongside their prince Rhaegar at the Trident. But they weren't merely guarding Rhaegar's wife. Ned and Howland were the only survivors of the fight.
In the Tower, Ned found his sister Lyanna dying from childbirth and her baby boy - Rhaegar's son - whom Ned would promise to adopt and raise as his own son, Jon Snow. Ned's cover story that Jon was Ned's bastard from a tavern wench is one that Ned would maintain to his grave. Not even his wife Catelyn, and especially not his best friend Robert, who would kill Jon if he knew Jon was really Rhaegar and Lyanna's son, would ever know the truth.
Gilly's discovery of a marriage record that proves Rhaegar and Lyanna were legally married, rather than Lyanna being his prisoner, means Jon Snow is not a bastard at all - he's actually a trueborn Targaryen! As the only survivor of Rhaegar's Targaryen line, Jon Snow has no claim to being King in the North (which by rights should now go to Sansa as the eldest Stark, since Bran abdicated the responsibility), but Jon does have legal claim to the Iron Throne! Jon may even have more claim to the throne than his aunt Daenerys, and certainly more than Cersei Lannister does. How any of this holds up legally, and whether one claim has more merit than another's is anyone's guess. War and bloodshed tend to be the primary way to settle such disputes in Westeros.
Thus far, neither Jon nor Daenerys are aware of these truth bombs and we don't yet know how any of this will affect their simmering will they/won't they attraction to each other. We also don't know if Jon being a trueborn Targaryen lends any credence to him possibly being the prophesied Prince Who Was Promised. However, when the truth comes out that Jon Snow has a right by blood to claim the Iron Throne of the Seven Kingdoms of Westeros, neither Daenerys nor Cersei will be best pleased by this important new player in the game of thrones.
Game of Thrones season 7 continues Sundays @ 9PM on HBO, HBO GO and HBO NOW.