Azor Ahai is a legendary figure who, 8,000 years prior to Aegon's Landing, defeated the Others (White Walkers) with a sword of fire called "Lightbringer." According to Melisandre, Azor Ahai will be reborn amidst salt and smoke to defend the world once again, this time from the Red God's nemesis, the Other. Melisandre clearly believes Stannis to be Azor Ahai reborn -- "the prince that was promised." However, Maester Aemon (Targaryen) believes it to be Daenerys, and many fans think it will be Jon Snow.
However, Victarian Greyjoy, Aegon VI Targaryen, and Rhaegar Targaryen are also considered to be Azor Ahai reborn. (Though when Robert killed Rhaegar, he doomed Westeros.) (Art courtesy of Amok