What does the abbreviation RSVP stand for and mean in an invitation?

It is a commonly used acronym for the French expression "Repondez s'il vous plait" which directly translates as "Please respond". What this means is you should advise your host (the person who sent the invitation) that you will or will not be attending the function, and if you are coming, whether or not you are bringing a guest (this is only allowable if the invitation indicates you may).