Hamster balls are hollow spheres made of clear plastic into which hamsters, gerbils, degus and other small rodent pets are placed, allowing them to run around outside their cages without the risk of running away, getting lost under furniture or in walls. They are designed to provide hamsters with exercise.
Wayne Coyne, the lead singer of the band The Flaming Lips, is indeed known to crowd-surf in a giant hamster ball. Hamster balls are a recurring subject on xkcd, starting with 152: Hamster Ball, which in direct relation to this comic showed that Cueball's biggest and only wish is such a ball.
The comic starts with a genie, who, having been freed from a magical lamp, grants the owner three wishes; this isn't unusual, since the idea of a genie who does this is a very common trope in the fantasy genre.