I suppose there is spoilers for Song of Ice and Fire and Game of Throne beyond this point.
It was not me who came up with the theory, for full on video on it, go here
But in short:
Rhaegar first believed he was Azor Ahai, so he trained himself to become a warrior.
Azor Ahai's first sword broke when it was tempered with water, Rhaegar died in the water's of the River land.
Rhaegar then came to believe it was his son (Aegon) who was Azor Ahai.
Azor Ahai's second sword broke when it was tempered with the blood of a lion, Aegon (together with his mother and sister) died at the hands of the mountain, commanded by Tywin, a lion.
Then Rhaegar finally believed Azor Ahai would be born by him still, but not by his Martell wife.
Azor Ahai final sword, Lightbringer, only came to be when it was used to kill Azor Ahai's wife.
Jon Snow's birth also happen to have killed his mother.
So Jon Snow is Lightbringer, the one who will bring the dawn, forged by Azor Ahai reborn, Rhaegar Targaryen after he failed to create Lightbringer in himself and his first son.