Julie,
there are actually a couple of options.
You can have your regular dinner on the beach. The waiters will take your normal dinner table from the dining room and put in on the beach outside under the palm trees and decorate your table with a flower arrangement - we did this for my husbands birthday and they even wrote happy birthday in coloured sand on the table. As you still eat the regular meal they serve in the restaurant all you pay is a set up charge which was $15 (£8).
You can also have a special al a carte meal served by waiters with a special menu which I believe is served at the swimming pool end of the Island - cost is around $45 per person.
lastly you can have a sunset dinner on a deserted Island where you go off with 3 or 4 other couples before sunset, have a glass od champagne as you watch the sunset and then have dinner on a private table on the beach - cost was $69 per person. We signed up for this but it didn't get run because not enough people signed up which was a shame as it was actually going to be run on my husbands birthday (they only do this once a week) so instead we just had the first option above and had a bottle of champagne instead.
Tracy