Why is there no gravity on moon?

There is gravity on the moon. Basically there is the gravity from the moon itself, which is (on the surface) about 1/10 of the gravity on the surface of the earth. Then there is the gravity of the earth, which makes the moon rotate around the earth (in one lunar month ~= 4 weeks). Lastly there is the gravity from the sun, which makes the earth + moon revolve around the sun in 1 year.

Everything with mass has gravity, but it is only measurable on a human scale if the mass is as large as the moon or the earth. Even the gravity pull from your fat neighbor kid is minuscule.