Ground:
It is a connection to provide the path for current to go back into source, as current can flow only if loop will complete. As every electrical circuit requires power source to drive it, it requires ground also to provide current path;
Earthing:
Earthing is provided with electrical equipment metalltic body parts, which should not be connected to any circuit elements. If accidently voltage source will be connected to body of equipment, earthing will provide a low resistance path to flow the current and ensure that body will be at zero potential. It is just for safety measure so that if some one is touching the body, he should not suffer with electrical shock.
Umesh.