AND is the default. That is, a search for dog and cat returns all messages that contain those words anywhere.
QUOTES (") allow searches for phrases. That is, a search for "dog cat" returns all messages that contain that exact phrase, with space.
MINUS (-) eliminates words. That is, a search for dog and -cat returns all messages that contain dog but not cat. You can MINUS a phrase in QUOTES, like dog -"siamese cat".
The engine is not case-sensitive and searches the title, body, and author.