It stands for Répondez S'il Vous Plaît, a French phrase which means "Please Respond" or literally, "Respond, if You Please". It means that when you receive an invitation, you must send your response to the host if you are attending the event or not. Most invitations come with a response card that the guests can mail right away while some have their wedding planner's number that the guests can call or send message to.
In Western countries, etiquette follows that if you receive a written invitation, you have to respond promptly. It is a simple courtesy for someone who is nice enough to send you an invitation.
RSVP is written on almost every invitation. This is so that the guests would know who to contact to inform if they are coming, how many are coming or if not, reason why they cannot attend the event. For weddings, this is very important since determining the number of guests coming will give you the idea of how much you need to prepare for food and drinks, how big the venue should be and how many seats are needed to be reserved.
Guests should understand that RSVP is not just a list of numbers on the invitation. It is there for you to respond and give the host your answer to the invitation. Unfortunately, this is not true in the Philippines. Even with the highlighted RSVP font in wedding invitations, guests still tend to neglect them. Out of all the weddings I have handled over the last 2years, I can still count how many guests responded to RSVP. I don't know if it has become a practice but couples, to ensure that they will have enough space for the guests and enough food to eat at the reception, usually hire wedding coordinators to do the RSVP.
This may probably not a custom in our country but I think we can start learning the etiquette. Hosts have prepared so much for the event and would like for you to share their happiness. If you see an RSVP, grab your precious celphone and send your reply. It is that simple and it is but proper.