It's a small, inflatable cushion with a dock for the Wii Remote. So that when you rock/bounce the horse, the controller is able to register the movement. You are then supposed to hold the nunchuk as you would a horse's reins. If it were a horse. We'd imagine it could just as easily simulate the riding of a donkey, camel, llama, alpaca or Asian elephant.
Or if those animals aren't your style, maybe you'd be more interested in riding some examples Nintendo themselves provide in the actual patent, like bulls, burros (small donkeys), dolphins, whales, dragons, griffons, unicorns and giant eagles.
Griffons ? Awesome.
Nintendo's Patented Horseback Riding Wii Controller [Siliconera]