Someone who is queer doesn't identify with any sexuality or gender identity (typically specified as genderqueer).  

Reasons to identify this way may differ.  Some people relate to multiple sexualities or gender identities and find queer as the easiest explanation of who they are.  Others just don't want a specific label, so they use queer.  Queer is a broad term, so it is possible for two people to both identify as queer to not be anything alike.

"Queer" was once used as a slur against LGBT people, especially homosexuals.  Since then the word has been reclaimed, although some people still consider it offensive.