Explaining the R + L = J theory
The gist of the theory in question -- known around the internet as the R + L = J theory -- is that Ned Stark didn't actually father Jon Snow as his bastard, but merely raised by him for his deceased sister, Lyanna Stark. As the story goes, Lyanna was "abducted" (the grand cover-up version of eloped) by Rhaegar Targaryen and gave birth to Rhaegar's son in the "Tower of Joy" (an event Bran witnessed at the tail end of last season). That boy? Mr. Jon Snow. You can read the exhaustive explanation here, but basically Ned promised his dying sister that he would raise Jon as his own.
Enter Gilly, who's peppering Sam with random facts High Septon Maynard recorded -- the High Septon apparently was fond of writing down every time he took a shit. But among the steps and bowel movements, Gilly asks Sam to define "annulment" which Sam does without pausing to consider what Gilly is saying. She goes on to reveal that Rhaegar got his marriage annulled in Dorne, and was remarried in a secret ceremony. The Tower of Joy is on the northern edge of the Red Mountains of Dorne. See where this is going?
Without mentioning them by name, Gilly has discovered that Rhaegar's first wife, Elia Martell (RIP Martells) was officially cast aside in favor of Lyanna. Had Ned and Robert only known that Rhaegar had married the woman he kidnapped, they probably would've been cool with it and wouldn't have had to stage a rebellion to overthrow the Mad King, right?
All of this means Rhaegar -- who was the Mad King's son -- was Jon's legitimate father, and that Jon Snow is a legitimate heir to the throne, which means Daenerys is technically his aunt, which means maybe, just maybe, we'll get to witness another one of the incestuous relationships for which Thrones characters seem to have an uncanny affinity. Fun!