Question: I am new to physics and I understand *gravity* is a pulling force.

Let's assume a *ball* has been placed on the ground. Does *gravity* has any role after I placed an object (e.g. ball) on ground? 

Sorry, if I asked something silly or the question was wrong.

Answer: 
All object with mass has gravity. mass is the amount of matter in that object. 
That's why the weight of an object feels less on moon even if the mass is same. Earth's gravity is that force that attracts every objects towards its centre. Due to this gravity we could land on the earth surface even after we jump on it. without gravity, if we jump on the surface of earth we go upwards with uniform speed (neglecting air friction).
The force of gravity never stops acting on the object. However, the gravity is balanced out by an equal and opposite normal force. Gravity simply keeps the object stuck to the floor. It does not stop existing; it is merely balanced and therefore has no overall impact on the object's motion. Hope this helps! -Alm.