Physics is all kinds of broken. So you've got a bunch of little worlds that float through space in a grand cosmic dance that appears random, but has enough order to it that worlds never crash into each other. Worlds usually (though not always) have at least one miniature star orbiting them to give them light and heat. That's not the interesting part; that's just the setup. The interesting part is how people travel from one world to another: on each world, there are small pockets of reverse gravity, made visible by waterfalls that fly up into the sky (called waterrises). If you want to travel, you swim down a river and take off up the waterrise to launch yourself to another world. Of course, it's best to have a parachute, and even better to time it properly so there's another world passing by to land on, otherwise you may smack yourself into a star or float off into space for ages.
The distance varies, since the worlds are constantly shifting around. But overall, the distance and velocity would match so that a trip from one world to another would take anywhere from a few hours to a day. The worlds are also small enough that given such a distance, looking from the ground, one world might look like a moon to another.