Bunnies are the source of the game, Tunnel Town, and there are many types of them. They can be bought at McFluffin's Market, or bred with the Dance Floor. They will work for you when you place them on Gems, you can place them on interactable furniture, and will run around the burrow when they are free and unoccupied.
List of Bunnies
Bunnies also have levels, and must be level 4 to dance. To level them up, you can feed them Food that you have grown or bought. As you feed your hungry bunnies, there will be another bar at the top. That represents the exp your bunnies has and will rise, but not as quickly as your hunger bar.
One way to get them is to breed with the Dance Floor. A guide of breeding combinations: Breeding Guide