WARNING: This list contains massive SPOILERS for Season 7 of Game of Thrones.
Game of Thrones is a study in duality. Gilly's reveal in the Citadel, that some long-forgotten High Septon annulled the marriage of "Prince Ragger," was so small, you could be forgiven for missing it. It wasn't like the Children of the Forest creating the White Walkers or the discovery of dragonglass underneath Dragonstone. Those were big moments, scenes intended to make you notice and remember them. But, like in any good magic act, it's all about misdirection.
Gilly's discovery on Game of Thrones was meant to be glossed over by all but the most hardcore fans. After all, the announcement was presaged by facts even Samwell Tarly - a notorious glutton for knowledge - found dull (number of steps, number of sh*ts, etc). But to anyone who's been paying close attention to the series - or read the books - Gilly clearly unearthed the most important secret in Game of Thrones history.
The High Septon (almost definitely) preformed an annulment not for some unknown character named "Prince Ragger," but for Rhaegar Targaryen, the Prince of Dragonstone and heir to the Iron Throne. At least, he was before Robert Baratheon caved in his chest at the Battle of the Trident. Still, Gilly's discovery has massive implications for the future of Westeros and, indeed, Game of Thrones as a whole. Rhaegar may be dead, but his son is very much alive.
Gilly Is The Greatest Researcher In The Seven Kingdoms
Gilly probably has the most inspirational character arc in all of Game of Thrones. She started out as the illiterate slave-wife of an abusive father-husband and now she's doing research of her own volition in the center of all Westerosi knowledge, working with a kind man that she loves, and caring for a happy and healthy son. But it makes sense that she's willing to look at books no one else has thought to glance at. She brings a true outsider's perspective to the maesters' stronghold.
It's really no surprise, then, that Gilly managed to make the biggest discovery in Game of Thrones history. While reading a book on the life and records of a High Septon, she asks Sam what "annulment" means. It turns out, the High Septon she's studying performed an annulment for "Prince Ragger" (clearly a reference to Rhaegar Targaryen, Daenerys's older brother) and married him to someone else. The audience, however, does not get to find out who the prince got remarried to.
We Miss Out On Crucial Information Because Sam Can't Stop Mansplaining
Sam and Gilly, and by extension all of the characters on the show, miss out on the enormity of Gilly's revelation because Sam was busy not listening to the love of his life. After Gilly – who, remember, just learned how to read – can't get Sam's attention by either sharing interesting (to her) facts or engaging him with questions, Sam proceeds to interrupt her, shut her down, and mansplain his anger at the ,aesters' current system.
Sam completely ignores information that could lead to the salvation or destruction of Westeros, all because he was too busy to listen to a woman. Gilly, however, patiently listens to his rant, and they move on. Vigilant fans, of course, did not.