The Moon has less mass than the Earth, which means it has less gravity than the Earth as well. (Also, there is WAY less atmosphere—as in, pretty much none—on the Moon than we're used to having press down on us constantly.)
Since the gravity isn't pulling on us as strongly on the moon as it is on Earth, we can jump higher and further with more ease. That's because our muscles (and all other body parts involved, like our bones and joints and heart and lungs) all were developed and conditioned to work in the stronger gravity on Earth's surface.
