Gravity is the force or pull on Earth which keeps people and objects from floating away into space. Your weight is the amount of force that gravity has on you on Earth. If you were to travel to the moon, you would find that the gravitational pull is 1/6 the amount of that on Earth as the moon is much smaller in size.
Since the pull is smaller, your weight would be smaller as well. You would weigh 1/6 the amount on the moon as you do on Earth. Therefore, you would weigh and feel much heavier on Earth, than on the moon!