So what do they do? Well basically you put them down and they run (or rather wheel) around. Their actions have a degree of randomness built in and are sufficiently realistic to appeal to their target audience, which is children aged 4+.
There are also extras available to buy. The various Zhu Zhu pet accessories currently for sale include a funhouse, spiral slide and, of course, the traditional hamster wheel. In the words of Cepia: "Collect and Connect all of the Zhu Zhu Pets™ Hamster accessories to make a Humongous Hamster city!"
One of the reasons that Zhu Zhu pets are so popular is probably that they're affordable: list price is around $10. However this Christmas demand is outstripping supply and few stores actually have them in stock. So these little toy hamsters are apparently selling on auction sites for prices up to $60.