"When the red star bleeds and the darkness gathers, Azor Ahai shall be born again amidst smoke and salt."
The red star would be the comet, and the Others and the coming winter would be the darkness, like that of the Long Night. In her own interpretation of this prophecy, Melisandre claims that Dragonstone is the place of smoke and salt. She also claims that she has seen in the flames that Stannis is the Lord's chosen warrior, Azor Ahai reborn, and that she has seen him leading the fight against the dark. The flames do not lie, according to her, but even if she is not willfully misleading Stannis she may be misleading herself. Daenerys, after all, was born on Dragonstone.
More importantly, however, she was figuratively born again as the Unburnt at the time of Drogo's death and the first appearance of the red comet, where she wept salt tears and immersed herself in smoke and fire of the pyre.