Quaithe is Game of Thrones' biggest unresolved mystery and the subject of many A Song of Ice and Fire fan theories, but who was she and why does she matter? Played by Laura Pradelska, Quaithe only actually appeared in two episodes of Game of Thrones season 2, but left a big impression and an even bigger question mark behind.
In Game of Thrones, Quaithe made her first appearance in season 2's "The Ghost of Harrenhal", where she warns Jorah Mormont that the men of Qarth may desire Daenerys' dragons. It's not her words that stand out, however, but her appearance, with Quaithe instantly striking thanks to her gold hexagonal mask. She re-emerges a couple of episodes later, informing Jorah that all men who pass the Doom of Valyria need protection, and also questioning his own loyalty to Daenerys.
After that she's never seen again, but it becomes clear that she is in some way prophetic. Not only do the warlocks steal Dany's dragons, but in Game of Thrones season 5 Jorah himself sails past Old Valyria without protection, and ends up contracting greyscale. Quaithe foreshadowed both events, but isn't so much as mentioned after Game of Thrones season 2, leaving her true purpose unclear.
Quaithe has a bigger role in George R.R. Martin's A Song of Ice and Fire books, where she interacts with Daenerys directly, and makes even more vague prophecies. These include "To go north, you must journey south, to reach the west you must go east. To go forward you must go back and to touch the light you must pass beneath the shadow," and "The glass candles are burning. Soon comes the pale mare, and after her the others. Kraken and dark flame, lion and griffin, the sun's son and the mummer's dragon. Trust none of them. Remember the Undying. Beware the perfumed seneschal."
Both of these quotes have long been speculated over by A Song of Ice and Fire fans to divine their true meaning, from Daenerys' journey to just who the "perfumed seneschal" is, with some of them difficult because of the many possibilities. Still, some of these have already shown to come true, or are about to: the Kraken likely represents Victarion Greyjoy, who is sailing for Daenerys by the end of A Dance With Dragons; the lion is Tyrion Lannister, who is likewise on his way to Dany; the griffin and the mummer's dragon are presumably references to Griff and Young Griff, a.k.a. Jon Connington and Aegon Targaryen, and the sun's son was Quentyn Martell, although most of these didn't make it into Game of Thrones.
Still, while that means her prophecies and warnings are often accurate, it doesn't solve who she is. There are various theories, ranging from Ashara Dayne to Sheira Seastar, while the mention of "glass candles" suggests she might be working with the Maesters of the Citadel, especially as Archmaester Marwyn has a keen interest in Daenerys.
Whether there is a bigger reveal with Quaithe remains to be seen. There certainly wasn't in Game of Thrones, but Daenerys thinks about her much more in the books, and has a few visions of her too. But Quaithe's identity isn't what matters so much as her purpose, and in that we can be guided by the events of Game of Thrones, including season 8. Daenerys' downfall is one driven by a belief in her own destiny and right to rule, which is in part pushed by prophecy too, such as being The Prince (or Princess) That Was Promised. It's not the first time we've seen this kind of arc though, with clear parallels to be drawn between Stannis' story and Daenerys.
Stannis went down that path partially because he was being guided by Melisandre, and knowing where Daenerys' story is going, we can say that Quaithe is serving a similar function for Daenerys' story. Both characters are from Asshai, and in Game of Thrones the costumes were designed to echo each other, with Quaithe's mask mirroring Melisandre's necklace. To that end, then, Quaithe isn't just some random figure to spout prophecies. She's the Melisandre to Daenerys' Stannis: someone who helps light the way, but also a warning of things to come. Quaithe's words play in Daenerys' mind, including the betrayals she now expects. Martin likes introducing these magical, oft-mysterious guides for some of his most important characters (Jojen Reed for Bran is another, and again will eventually link to the Iron Throne), and that's what Quaithe is. Her key message isn't one of those strange prophecies, but when she tells Daenerys to "remember who you are."
Ultimately, it may not matter too much who Quaithe is or was, and there are enough secret identities already. What matters more is what she represents to Daenerys' story, in both Game of Thrones and A Song of Ice and Fire, helping to highlight the dangers of prophecy and destiny, while also contributing to her path of fire and blood. We've seen where it led Stannis, and Quaithe, by mirroring Melisandre, shows us where it's leading Daenerys.