RSVP stands for "repondez, s'il vous plait" or "please respond". A regrets RSVP is a formal way to let a host or hostess know that you will not be attending the event you were invited to. Sending a regrets RSVP is important so that no one is planning for your attendance to an event and buys extra supplies that are then wasted. It is polite to send a regrets RSVP either way but some invitations clue you in to whether a response is expected.
Respond immediately. The sooner you respond, the less stress on the host.
Use an RSVP card if included with the invitation and be sure to fill in all the necessary information.
Write your own regrets RSVP if a card is not included. It is important to respond in the tone of the invitation. For example, if you were sent an informal invitation to a birthday party, you could respond with "I'm so sorry I can't make it to the party but I will be out of town. Have a great time and happy birthday. Emily".
Respond formally if the invitation is formal. The proper wording for a formal regrets RSVP uses formal names and language. For example: "Ms. Kate Hamilton regrets that due to a prior engagement she is unable to accept the invitation of Mr. and Mrs. Brian Gilbert for Friday, the seventh of October."