Jon Snow knows nothing, but you can learn everything about the potential secrets of everybody's favorite Stark bastard by watching this fantastic video, which happens to be the best explanation of the "R+L=J" fan theory I've ever seen. Probable spoilers ahead (especially if you're only watching the show)!
The theory, of course, is that Jon Snow is in fact the secret child of Rhaegar Targaryen and Lyanna Stark, and not her brother Eddard's bastard. The video, made by Alt Shift X, clearly recounts all the textual evidence — from Eddard's personal memories to what we know about the events that happened at the Tower of Joy and Lyanna Stark's death (which aren't much). Even if you know the details, it's a great refresher on all the reasons why "R+L=J" is A Song of Ice and Fire's #1 fan theory — and there's always the possibility that you missed a clue, too.