In a blink-and-you'll-miss-it moment, Gilly revealed something huge while reading aloud to a distracted Sam. She came across a little tidbit of information about the former crown prince Rhaegar Targaryen (Daenerys' older brother) that elucidated what happened between him and Lyanna Stark all those years ago. Everyone thought he abducted her, but were Rhaegar and Lyanna married on Game of Thrones?
While she was reading over old tomes of the maesters, Gilly revealed that High Septon Maynard performed an annulment of Prince Rhaegar's marriage and remarried him to someone else at the same time in a secret ceremony in Dorne. You know, the kind of highly sensitive and confidential information that you jot down in your personal diary in the hopes that no one ever reads it after you're dead.
Though the show skimmed over the moment fairly quickly (and Sam certainly didn't take much interest in it), it's incredibly important. Many had assumed that Rhaegar had taken Lyanna against her will and kept her captive, a belief held especially by Lyanna's family and her ex-fiancé Robert Baratheon. But even if the relationship had been consensual, one would assume Rhaegar and Lyanna wouldn't have been able to make it legal because he was already married. However, this proves otherwise.
Rhaegar and Lyanna's relationship was the catalyst that set off a chain of events that is still playing out in the series. When Lyanna's father and brother went to King's Landing to try and get her back, Mad King Aerys burned them alive. Assuming that Rhaegar had run off with his bride was what caused Robert to launch his rebellion and eventually rule Westeros as a king, all of the fighting for the throne spawned off that one moment. And now it's clear that Rhaegar and Lyanna were legally married, and very likely in love.
Which was unfortunate for Rhaegar's first wife, Elia Martell of Dorne. Her life was nothing but tragedy, it seemed; her husband abandoned her for another woman, then she and their children were violently murdered in the sacking of King's Landing. While Elia was being killed, Lyanna was in Dorne at the Tower of Joy, preparing to give birth to her and Rhaegar's only child. That child, of course, is Jon Snow. And the fact that his parents were married changes everything.
This means that Jon is legitimate, and not a bastard as he had always believed. It also means that he has a real claim on the Iron Throne. As the last living son of the crown prince, the throne would pass to Jon even before it would pass to Daenerys, the presumed last Targaryen. (Gotta hate that patriarchy.)
If and when Jon finds out about who he is, it could create some real friction between him and the Mother of Dragons. And by this point we've learned: On Game of Thrones, the truth eventually comes out.