On Sunday night, Sam may have been too preoccupied with his own problems to listen to Gilly — but Game of Thrones fans' ears certainly perked up when she discussed Rhaegar during "Eastwatch." In between documenting the number of steps at the Citadel and the number of bowel movements he had, High Septon Maynard wrote that he provided an annulment for Prince Rhaegar, and then performed a secret wedding ceremony for him. Although it wasn't explicitly stated, the assumption is that Rhaegar Targaryen wed Lyanna Stark in that ceremony, meaning that Jon's parents were married on Game Of Thrones. And, with this marriage, the King in the North is a legitimate Targaryen and has a stronger claim to the throne than Daenerys.
Daenerys was raised believing that she and her brother Viserys were the only surviving members of the Targaryen bloodline. After Khal Drogo took care of Viserys by giving him the gold crown he so desired, Daenerys was then supposed to be the last Targaryen left standing. And while the revelation during the Season 6 finale that Jon was Dany's eldest brother Rhaegar's child was enough to prove that Jon was a Targaryen, him being legally born into the family adds an entirely different dynamic to the line of succession — and it's not good news for Dany.
Using the traditional patriarchal line of succession, Jon being a Targaryen means he has a stronger claim to the throne than Daenerys — but that was only if people ignored that he was a bastard. Now that he is Rhaegar's legitimate heir, there's no denying that Jon is technically the rightful ruler. While Daenerys won't be pleased with this information, she'll perhaps be more OK with it now that she has actually met Jon and seen what a stud, errr I mean, what a worthy ruler he is. However, since Sam was all angry when Gilly revealed this information that is a major deal about his best friend Jon, how would Dany even find out that she's not as entitled to be the queen as she thinks she is? Furthermore, how is Jon supposed to learn any of this?
Well, even without seeing Bran in his new Three-Eyed Raven state, Jon didn't question how his younger half-brother (really, his cousin) was able to see the White Walkers approaching Eastwatch. Of course, Bran's raven message supported what Jon had been saying to anyone who would listen, so he didn't inquire where this information came from. Jon wasn't skeptical about Bran's vision. But if and when Bran eventually tells Jon that he's really the son of Lyanna Stark, not Ned Stark, will Jon be so willing to believe? I could see his humility getting in the way of him accepting that he was destined for greatness, which is absurd — but oh so like Jon Snow — considering all the greatness he has accomplished while believing he was an unworthy bastard.
As for being worried that Sam will never make the connection between Rhaegar and Jon, Bran can see everything from the past, present, and future. So while viewers only saw him gaining the information that Jon is Lyanna's son, he should know the full truth of Jon's parentage. But will anyone believe Bran's history lesson? Without seeing Bran for yourself, it's hard to accept that the last surviving Stark son is some mystical, all-seeing figure. And considering Bran was believed to be Jon's brother up until now, Daenerys might think this is all a ploy to stop her from achieving her goal.
Yet, if Daenerys is honest with herself, she'll realize she just witnessed evidence that Jon is a Targaryen. She looked extremely intrigued when Drogon allowed Jon to pet him, but it only seemed to make her even more attracted to Jon. She should probably clear her head and ignore the pheromones (he's your nephew!) and really think about why that happened when no one else has ever been able to approach her dragons like that. Her Targaryen blood has allowed her to become the Mother of Dragons and it runs in Jon's veins too.
For fans who are disappointed that Jon now has a better claim to rule over Westeros than Dany, it's worth considering that he could step aside and let her rule. Although Jon is a natural leader, he doesn't crave power like Daenerys does and would possibly defer to her. If that's a bit too rose-colored for your liking, well then, there's also the possibility these two could get together and create the ultimate power couple of Ice and Fire and rule together as king and queen. This would be ideal except for the fact that any romantic relationship between these characters would be incest. But if you can get past that (I currently cannot), their marriage could negate the line of succession since Jon could presumably treat his queen as his equal.
While Daenerys discovering that she does not have the strongest claim to the throne will not be pretty, it doesn't have to end in disaster since she now acknowledges what a good person Jon is. If she can look past her own ego, she could be happy knowing that she has another relative, who is as admirable as she is. However, with this being Game Of Thrones, Jon being a legitimate Targaryen won't be without some negative consequences. But these Targaryen relatives coming together is essential to the story and no matter who is first in line, Jon and Daenerys were born to lead and hopefully, bring peace.