It's called the re-hitching ceremony, and you can usually find information about it on many WDW info sites. If you made a note of it when you made your priority seating, make sure you also mention it when you get to the Garden Grill restaurant check-in podium.
Basically, here's the gist. The "reverand" shows up at your table with best man Mickey, and then proceeds to go through with an informal wedding vow renewal. Afterwards, there is a fun surprise for the participants that has everyone in the vicinity involved (hope you can count to 100 while kissing).
I'll also be doing it with my DW in May, and she has no clue, so you can probably keep it a surprise.
Good Luck
