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? Etiquette rules followed in most Western cultures require that if you receive a formal, written invitation, you should reply promptly, perhaps that same day. For hosts who are planning a dinner party, a wedding or a reception, this is important from a practical point of view, because they need to know how many people to count on and how much food and drink to buy. More important, though, is 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, invitations often carry a "regrets only" notation at the end. That means that the host will count on your being there unless you 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?"
You might wonder why we use the initials of a French phrase in an invitation that is written in English. You could say that the French "invented" etiquette, although that would be a simplification because there have always been rules of courtesy to follow in civilization. In fact, an Italian diplomat, Conte Baldassare Castiglione, wrote the first book about proper behavior among nobility in the 16th century. Many of the practices of Western etiquette, however, came from the French court of King Louis XIV in the late 17th and early 18th centuries. At Versailles, his palace, Louis XIV had the rules for court behavior written on what the French referred to as "tickets," or "étiquette." The tickets either were signs posted at Versailles or were the invitations issued to court events with the rules of behavior printed on the back; experts give different versions of the origin. And French was the language of refinement and high society through the 19th century in the United States. Judith Martin, the author of etiquette books and a syndicated newspaper columnist known as "Miss Manners," thinks that "R.S.V.P." came about as a polite way of reminding people of something that they should already know: If you receive an invitation, you should reply.
Here are some interesting links about etiquette: