This is just a logic after reviewing the last seasons of the story.
In the flashses of Bran Stark, he saw young Ned Stark rescued his sister “Lyanna” from a fortress but she died after giving a birth to a son. Her final words to Ned was “Promised me Ned”
Lyanna was married to Robert Baratheon. But Rhaegar Targaryen (the eldest son of mad King – eldest brother of Daenerys Targaryen) kidnapped the beautiful Lyanna and raped her and imprisoned her in a fortress. This led Robert Baratheon wages war against Mad King and in the battle Robert Baratheon killed Rhaegar Targaryen. Later Jamie Lannister killed Mad King and Robert became the king and married Cersie.
That son which Lyanna gave to birth must be the son of “Rhaegar Targaryen” which was a result of the rape. That’s why Lyanna asked Ned Stark not to tell Robert about the child. If Robert knew that the father of the child of his beloved wife is Rhaegar Targaryen, he would kill the child.
So Ned Stark took the baby to the north and told Catalyn that the child was his bastard son and named him Jon Snow.
If Jon Snows parents are Lyanna Stark and Rhaegar Targaryen, he is half Stark and half Targaryen. Jon is the only son of Prince Rhaegar Targaryen who were to be the king after Mad king. So he is the true heir to the Iron throne. Daenerys Targaryen is his aunt (Even though they both are young).
Jon Snow is half dragon blood. That’s why he is hard to kill and came alive even after the death. That’s why white walkers fear him. That’s why Red Woman chose Jon Snow as her master.