Throughout five seasons on Game of Thrones, Jon Snow is called as the bastard son of Ned (Eddard) Stark. Bastard son means he was born out of wedlock vows.
Spoiler Alert!!! Season 6 “episode wind of Winter” hinted that Jon Snow is not a bastard son of Ned Stark at all. He is the son of Ned’s only sister Lyanna Stark and Rhaegar Targaryen, Daenerys’s older brother. That means he is the nephew of Daenerys Targaryen.
But Lyanna was engaged with Robert Baratheon, king, and Ned Starks close friend. Rhaegar must have kidnapped Lyanna for her beauty. But in this scenario also Jon becomes a bastard son of Rhaegar Targaryen.
When Bran Stark visits Tower of Joy through his vision, he saw his father battle with Rhaegar Targaryen. Rhaegar was protecting Lyanna and his still unborn son. He died in this battle, he almost killed Ned Stark but saved by Howland Reed (father of Meera and Jojen Reed). That means, Lyanna and he were in love, then eloped during Roberts’ rebellion and then married. Plus, plural marriages are allowed in Targaryens. So that makes Jon a legitimate son of Rhaegar.
Ned makes the promise to Lyanna that he will protect her son from Robert. Robert wanted kill all Targaryens decedents so that no body comes up for Iron Throne claim and that is why Ned called Jon his own bastard son and kept secret from all including his wife Catelyn Stark.
Now this opens a lot twist in the story. We need to see that in GoT season 7. Now Jon is a legitimate contender for Iron Throne. Plus he is having Targaryen blood running in his veins it means he might be immune from fire and he can tame and ride dragons. All these points will make season 7 more amazing. Eagerly waiting for Game of Thrones season 7. What about you?