Jon Snow's lineage was debated for years on Game of Thrones, with fans picking apart any little clues they could find to figure out the identities of his real parents. The most popular theory was that Jon was not Ned Stark's bastard as he'd been led to believe for his entire life. He was actually Ned's nephew: the child of Lyanna Stark and Rhaegar Targaryen. Targaryen children were not welcome in Westeros following Robert's Rebellion, so the truth of Jon's birth became Ned's most closely guarded secret. Season 6 finally confirmed that theory, though Jon's Targaryen ancestry raises some interesting questions. For example: is Jon Daenerys' nephew on Game of Thrones?
The answer to that is a resounding yes, though the series hasn't made it crystal clear quite yet. The flashback to Jon's birth only showed Lyanna moments before her death, with Rhaegar nowhere to be seen. However, shortly afterwards HBO released a family tree infographic to clear things up. The graphic showed the many complicated connections between the characters on Game of Thrones and listed both Rhaegar and Lyanna as Jon's parents. And because Rhaegar is Daenerys' older brother, that makes Jon her nephew — which could make things tricky when Jon and Dany eventually cross paths.
Jon and Dany have become a popular ship in the Game of Thrones fandom despite the fact that they have yet to interact onscreen. It's easy to see why people might root for them: they're fan favorite characters with nice faces who are around the same age and aren't totally morally bankrupt (a rarity in Westeros). However, their familial connection could put the kibosh on anything romantic between the two of them, though neither are currently aware of it; only Bran and the audience know the truth.
But even without the romantic possibilities, Jon's existence could be perceived as a threat on Dany's claim to the throne. In Westeros, power passes from father to son in the ruling family. Rhaegar died before he could be crowned king, but as the firstborn son he would have inherited the throne from his father Aerys. As Rhaegar's only living son, Jon would technically be next in line. This could result in issues between Jon and Dany theoretically, though he'd be unlikely to try and steal the power from her.
As the focus narrows on Game of Thrones in its final two seasons, it seems clear that Jon and Dany will have a major impact on each other's stories going forward. Just what form their relationship will take remains to be seen, but I'm hoping they don't take any tips from Jaime and Cersei.