Spoilers if you’re behind on the show.
She had previously believed Stannis was ~the one~, which was one of the reasons she was so disillusioned by his failure at the end of last season.
Several characters talk about the prophecy of "the prince that was promised" in the books, and Melisandre also uses the name Azor Ahai in connection with it. While some fans believe these are two separate prophecies, there's a lot of overlap and it makes sense that they're about the same hero.
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According to prophecy, he will be reborn after a long summer, when an evil darkness spreads over the world. This is obviously significant to the current events in Westeros, what with WINTER and the GIANT FREAKING ICE ZOMBIES ready to unleash themselves on the Seven Kingdoms. Many believe the prince that was promised/Azor Ahai is the key to defeating them. Rhaegar Targaryen also says "his is the song of ice and fire" a.k.a. the name of the whole damn book series. So, you know, pretty important.