David Letterman’s crew loves him so much that they want him to be up to date on all the latest advances in technology. So they added a button to his chair and tempted him to push it to see what its special feature is. Well you know what is going happen next, but it is still fun to watch over and over and over again.
BTW I heard that once he returned to The Late Show, he wrapped that special chair up and sent it to Jay Leno as a gift.