Why is it easier to lift and carry heavy object on the moon than on earth?

When you jump, you exert a force greater than the force of gravity to achieve a net positive upward acceleration - at least until your feet leave the ground and you quit exerting force. The net upward force is

Fnet = (force you push off with) - (force of gravity)

Because the moon has less mass than the earth, the force of gravity is less. As a result, the force you exert to jump on earth would give a higher net upward acceleration on the moon and allow you jump higher. Even with the extra weight of their space suits, the net upward force they can generate is more than they could when jumping without their suits on the earth.