So, as far as I can tell:
1. Back in the day, miss great-aunt was sweethearts with a girl she went to school with. They weren't coming out and saying it directly, but it seemed pretty romantic (and doomed, because of marriages and stuff).
2. Then she died (in a kind of silly way).
3. The other girl must at some point have also died
4. And been reincarnated as the current-time live girl who can see her,
5. And who has dreams about the past life, and still/again loves her
6. And who really wants her to stick around as a ghost so they can be kind of together instead of going to heaven, so she doesn't want her to remember the past stuff and get anything resolved.
7. I don't really understand what the ghost marriage part is about. Since none of the characters do either, I'm assuming that's OK and will be explained to some extent in due course.
Anyway, it's pretty cool. Interesting balance of sorrow with a bit of comedy and flippancy.