When you open it, inside is a wooden replica of the poisoned apple from Snow White. Printed across the face are the words, "Snow White - An Enchanting New Musical".
An Enchanting Musical was a Snow White stage show that ran back in 2004-2006 at Disneyland (see earlier posts). The apple and box look to be a promotional set, possibly produced for opening night or some VIP press event around the premiere.
Images courtesy of the Keith Hively Collection.
NOVEMBER 2016 UPDATE:
Keith's apple box has gone up for auction and can be found here: Item no. 815.
Images via VanEaton Galleries' Souvenirs of Disneyland auction.