The other exhibit is Kate Middleton's Wedding Dress. As HM The Queen said to the Duchess of Cambridge when she inspected the exhibit - it looks like a ghost!
It is on a stand in the centre of the Ballroom with the veil and diamond Cartier 'Halo' tiara suspended above it. There is a video about the making of the dress, behind glass a panel of the lace to be examined and a chance to walk around the stand to get a good look at the dress.
Buckingham Palace is open to the public until 3rd October and tickets really are a 'hot ticket' item this year so it is advisable to book early.