R.S.V.P. stands for "répondez, s'il vous plaît". It is a French phrase which means "Please Respond" or literally, "Respond, if you please".
This phrase is mostly included in almost any invitation but is most likely being seen in wedding invites. Why include it? Generally, the person who sent the invite would want to know if the guest will be coming to the event or not. This is so that they know how many people to count and how much food and drinks are needed to be prepared as well as the seats to be reserved.
Most wedding invitations come with a response card that guests can mail right away while others have the host's number or their coordinator's number where guest can call or send a message of confirmation. Ideally, guests are required to respond to the R.S.V.P and of course, it is a simple courtesy to send a reply to someone who is nice enough to invite you. Send a notice even if you are not coming to the event so that the host will not be left hanging with your answer.
In most Western countries, etiquette follows that if you received a written invitation, you have to respond promptly. I hate to say this but in some countries, R.S.V.P is nothing but merely additional numbers written in the invitation. Guests are not obligated to respond. At times, event coordinators are the one sending messages and calling the guests to ask if they are accepting or declining the invite.
For guests reading this post, piece of advise - do RSVP to the invitation. Hosts prepare much for their event, responding is your way of thanking them for inviting you.