Ok...the story is that Lyanna Stark was hooking up with Robert Baratheon until she was stolen by Rhaegar Targaryen, thus setting all of the pre-events of the Game of Thrones in motion.

That flashback showed that Lyanna died during childbirth....

Ned Stark came back from battle one day with a baby. He told his wife that he had a fling in the war....then raised the child as one of his family members carrying the name SNOW because, as a mistresses' child...he cannot take on the name STARK.

Well...that child wasn't a SNOW or a STARK....it was a TARGARYEN and his sister's dying wish was that he keep it a secret from Robert or Robert would kill the baby.

So...Ned inherits a bastard child, tells Robert the baby died along with Lyanna, and takes the weight on his marriage to honor his sister.

Notice how the scene cut immediately to Jon's face

D