RSVPR.S.V.P. stands for a French phrase, "répondez, s'il vous plaît," which means "please reply." The Invitee sending the invitation would like you to tell him or her whether you accept to come to the event or you are declining the invitation. That is, will you be coming to the event or not? Etiquette rules followed in Western cultures require that if you receive a formal, written invitation, you should reply promptly, perhaps that same day. For hosts planning a wedding or a reception, this is important, because they need to know how many people to count on and how much food and drink to buy. More important, the simple courtesy of responding to someone who was nice enough to invite you, even if it is to say that you regret that you will not be able to attend.
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 you can call with your reply, although under strict etiquette rules, a written invitation requires a written reply. Nowadays, it is quite common to use "regrets only" notation at the end. That means that unless told otherwise it will be assumed that you will be coming. Some people even use "R.S.V.P." as a verb, as in "Have you R.S.V.P.ed to that invitation?"