From what I understand of Days specifically (and anyone feel free to correct me on this, I haven't played the game in years), it goes like this. Warning: Spoilers for Chain of Memories, if you're new to the series and haven't played that yet.

Xion is an intended side effect of Namine messing with Sora's memories during CoM. The Org's plan was to not only incapacitate Sora for good by fracturing his memories, but in the process create 2 Nobodies out of him, who would both be very competent Keyblade wielders.

As Sora's memories are slowly restored, Xion becomes increasingly weaker, because those fractured bonds that kept her existing are disappearing. She held memories/bonds related to Sora that were vital to Sora's restoration, which is the cause of the final fight at the Twilight Station: She and Roxas both know she needs to stop existing in order for Sora to come back, but Xion doesn't make it easy.

As for why Xion has the appearance she does, I haven't a clue.

But TL;DR, she's a weird second Nobody of Sora's, and once that paradox is remedied it's as if she never existed at all(?)

Again, anyone more versed on this part of the timeline feel free to correct me, I haven't touched Days since actually going through it on release.