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: 
yes: the gravity maintain the ball on the floor. And if the ball is soft, it is maintained squeezed.
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.