If you traveled from Earth to the moon, the measurement that would change is your weight.
Weight is the force exerted on an object due to gravity, and since the moon's gravitational force is about 1/6th that of Earth's, your weight would be significantly less on the moon.
Your mass, on the other hand, would remain the same regardless of your location, as mass is a measure of the amount of matter in your body and does not change with gravity. Your density and height would also remain unchanged.