Earthing is a safety measure to prevent electric shock or damage to equipment by providing a low resistance path for electric current to flow to earth in the event of a fault. For example if there is an electrical fault in an appliance such as a cooker then the fault current flows to earth through a protective conductor. A protective device such as a fuse or relay switch in the consumer unit switches off the electric supply to the cooker rendering it safe.
Bonding is simply a term used for connecting together all the metallic parts that are not supposed to be carrying electric current to the same electrical potential. This means that no electrical current can flow between these parts. The primary reason for bonding is to prevent a person getting a shock when they touch two metal pieces of equipment at different potentials. By earthing these bonded elements it protects people and equipment from harmful electrical faults.