As soon as Melisandre saw that her magic had worked and Jon Snow was living and breathing once more, she immediately jumped onto the next thing: her long-awaited, long prophesied Prince That Was Promised. That prince is possibly also Azor Ahai, a mythical warrior who once saved the kingdom from immense threats. Is Jon Snow the Prince That Was Promised on Game of Thrones?
For years, Melisandre thought that Stannis Baratheon was her promised prince, the reincarnated warrior who would save Westeros from a new age of darkness. When Stannis was killed, Melisandre lost both her purpose and her faith, and Season 6 found her at her lowest point. However, when she was able to bring Jon Snow back to life, Melisandre seemed reenergized. She immediately questioned Jon about what he saw on the other side, and then brought up her oft-mentioned Prince That Was Promised. Now that Stannis is gone, she seems to believe that's definitely Jon. Jon, however, might not be so certain. He's only been back for a few minutes, after all.
While there is evidence that Jon might be the Prince that Was Promised (or Azor Ahai; some feel the names are interchangeable and some do not), it's not certain for sure yet.
Jon is having a hard time with his return, understandably, but he's able to get back to business at hand fairly quickly. Melisandre's questions to him come right after he woke up, so it doesn't exactly result in an in-depth discussion. Jon is still reeling from being back at all – then remembering the betrayal that got him killed in the first place. He's confused, troubled, lost. It's a very season six of Buffy the Vampire Slayer moment.
But Melisandre definitely seems to have found her purpose in Jon. "The Lord let you come back for a reason," she told him. "Stannis was not the Prince That Was Promised, but someone has to be." Mel doesn't make an appearance for the rest of the episode, but it seems likely that her involvement with Jon isn't done, especially if she's convinced that he has such a powerful destiny awaiting him.
But first, thanks to Davos' encouragement, Jon has to pull himself together and face the men who betrayed him. He has to do his best to clean up the mess that was left behind when he (briefly) died. Whether that journey will grow to include him picking up a flaming sword and battling all the threats facing Westeros remains to be seen.