Earth binds the atmosphere because of

Earth is surrounded by an atmosphere of gases (air).

The reason is that in earth's atmosphere the average thermal velocity of even the highest molecules at the maximum possible temperature is small compared to escape velocity which in turn depends upon gravity. 

$\left(v_{e}=\sqrt{g R_{e}}\right)$

Therefore, the molecules of gases cannot escape from the earth. Hence, an atmosphere exists around the earth.