RSVP is the abbreviation for the French phrase "répondez, s'il vous plaît," which means "please respond." The abbreviation is used on invitations when the host needs a count of how many people plan to come to an event.
Using RSVP in France is currently considered old-fashioned and is rarely used. "Réponse souhaitée," meaning "please respond," is the preferred expression and is typically followed by instructions for how to respond.
When RSVP is on an invitation, it is common courtesy to respond to the invitation to ensure that the host has the proper amount of food and drink at the event.