I was told that if you theoretically jump down from a three-floor building (assume 10 m) on the Moon surface, you will equally break your bones as in if you were doing that on Earth. I do not know why would this be true: the acceleration due to free fall on Moon is significantly smaller, thus the final v shall be smaller than v on Earth. Would you be perfectly fine if you jumped down a 10 meter building on Moon?
It is certainly not the same.
Gravity on the Earth's surface is 9.81 m/s2. Assuming no upward or downward initial velocity, this means your velocity at ground level falling from 10 m is about 14 m/s (
sqrt(2 * 9.81 * 10)).
Gravity on the Moon's surface is 1.625 m/s2. The same fall will result in final velocity of about 5.7 m/s (
sqrt(2 * 1.625 * 10). This is equivalent to a fall on Earth from about 1.6 m (
5.7 ^ 2 / 2 / 9.81).
Assuming you don't land on your head, you should be okay.
If you come from Earth and make the jump, you'll be okay as the other answer says. But if you were to live full time on the moon or in space, your body would adapt to the weaker gravitational field, resulting in muscle mass loss and other effects - if these included changes to the bone structure, such a jump could be dangerous after six months or so.
It would be worth reading about the physiological changes to the MIR cosmonauts and ISS inhabitants to understand better what happens after a few months to a year - and how exercise programs mitigate the effects - but extending the lessons to multiple years or a lifetime in reduced gravity would probably be speculation.