"RSVP" stands for the French phrase, "Repondez, s'il vous plait," which translates to "Respond, please" in English. When the phrase is on an invitation, it means the hostess is requesting the invitee to let her know whether or not he plans to attend the event.
Events for which an invitation might request an RSVP include holiday parties, weddings, business conferences and movie premieres. It is considered bad etiquette not to respond by the requested date, because the hostess or event planner may need to know how many people are coming in order to make catering and seating decisions. In some cases, an invitation asks for "Regrets Only," meaning the invited guest only needs to respond if unable to attend.