How so? It only tells us that at least one of Jon Snow's parents must be a Stark (=Ned's blood). Either Ned or Benjen is his father, or Lyanna is his mother. Why did Benjen join the Night's Watch? What really happened to Lyanna? Did Ned truly abandon his honor and commit adultery to conceive Jon? These are questions that haven't been answered in the show yet, so we can't know for sure.
I've read the books, but I'm looking at this here in light of what the TV show has told us, and what can be deducted from that and common sense.
If Ned is the father, then the mother is probably this Wylla woman Ned told Robert about. If it's not then she at least has to be somehow involved (wet nurse?), or maybe to cover for some other mother, who's identity could not for what ever reason be revealed to anyone. Maybe it was some married highborn lady who's husband might not like the idea of his wife giving birth to some other man's son?. The husband was probably away for the war (Robert's Rebellion) so he might not know about his wife being pregnant.
If Benjen is the father, then maybe he joined the NW because the mother was somebody he shouldn't have been having those kind of relations with and Ned decided to cover for his brother and took Jon as his own bastard to maybe protect both Benjen and Jon from possible retribution from the mother's husband? The mother would probably be some highborn lady, and not Wylla, who simply could have been a wet nurse who was paid to be in on the ruse.
If Lyanna is the mother, then who's the father? Once again like with Benjen, Ned claiming Jon as his own bastard would probably be to protect Jon from some threat, but what could that be? I could see Ned tarnish his own honor for his family's sake (Lyanna or Benjen) so claiming Jon as his bastard would actually be honorable. Knowing that Robert hated Rhaegar Targaryen for something he did to Lyanna so much that Robert wanted every Targaryen die could imply that Jon's father could be a Targaryen maybe even Rhaegar himself. Ned would then definitely conceal Jon's true parentage from Robert, and to do so he would have to conceal it from everyone including his own wife.
I'd guess that Jon is not Ned's bastard. Both the Benjen and the Lyanna options seem more likely. Of those two Lyanna is more plausibe, since Ned has kept the secret for this long. With Benjen at the Wall, letting it out that Jon is in fact his would no longer be such a big deal, unless the mother is a Targaryen, then Robert's hatred would still be in force.
I hope we get some more info on this despite Ned taking his knowledge to the grave. Maybe there's somebody else who knows the truth.