R.S.V.P. stands for a French phrase, "répondez, s'il vous plaît," which means "please reply." The person sending the invitation would like you to tell him or her whether you accept or decline the invitation. That is, will you be coming to the event or not?
Many wedding invitations come with a response card that you can mail back right away. Other written invitations will carry the host's telephone number so we can call with our reply, although under strict etiquette rules, a written invitation requires a written reply. Nowadays, invitations often carry a "regrets only" notation at the end. That means that the host will count on our being there unless we tell him or her otherwise. Some people even use "R.S.V.P." as a verb, as in "Have you R.S.V.P.ed to that invitation?"
It comes from the French court system of invitations and that was adopted in the 1700's by George III in the English court because it was it was seen as very chic. And French was the language of refinement and high society through this time to the 1800's. :-) It held its niche appeal from then on, indicating it was only used by the nobility. It is still used by higher echelons of society on their invitations.