It means 'go ahead!' And there are a couple of meanings. The literal meaning is to invite someone to share in your hospitality. "May I borrow your book?" "Please, be my guest." The other way it is often used is to mean "you can go ahead, but I don't want to." "Should we dip these onions in chocolate?" 'Be my guest." "who will eat the last cookie?" "be my guest!"

zooey is right, i can only add that this is also used to threaten someone, you might have seen it in action movies like this: the good guy is a karate expert and already has beaten up the crap out of all the bad guys except for one. this last bad guy doubts if he should attack or not, then the good guy looks at him and says: "come on, be my guest!" (meaning: just try to attack me and i will kick your ass) the bad guy loses his confidence and runs away scared. i hope i didn't confuse you with this, but you might have probably seen it in some movie, its' a cliche