Stone and earth attract each other with an equal and opposite gravitational force. But, the mass of the earth is very large as compared to the mass of the stone. The gravitational force acting on the earth produces a negligible acceleration in the earth due to its high mass. Whereas mass of the stone is much smaller as compared to the earth, therefore, the same force produces a considerable acceleration in the stone. That's why we are able to see a stone moving towards earth but not earth moving towards the stone.