In Episode 3, Season 6 of Game of Thrones, one of the first things Melisandre says to the new(re)born Jon Snow is that he is probably the prince that was promised.
If you're a show-only fan, it may be easy to miss the significance of this plotline: Many book fans believe the "prince that was promised" is going to be the central figure by the end of the series.
Basically, Azor Ahai is a mythical figure in Melisandre's religion. He's said to be a great hero who fought against the darkness with a flaming sword called Lightbringer, which he forged by piercing the heart of his true love, Nissa Nissa.
The prophesied signs of the prince that was promised include:
* They are the blood of the dragon (and some believe, more specifically, a descendant of Aerys II and Rhaella Targaryen).
* Born amidst smoke and salt.
* Born beneath a bleeding star.
* Will wake dragons out of stone.
* Will draw Lightbringer from the flames.
* Will possibly have to make a sacrifice.
Now, there is an Azor Ahai theory about pretty much every character in the series, but the two strongest candidates are by far Jon Snow and Daenerys Targaryen.
Let's look at the evidence, shall we?