Many appliances have a metal case. If a fault lets the live wire touch the case, the case becomes live and could give a person an electric shock. The earth wire prevents this. It connects the metal case to earth and carries no current in normal use.
In a fault, the live wire touches the metal case and a large current flows through the earth wire to earth. This large current makes the fuse melt. A fuse contains a thin wire that heats up and melts when the current is bigger than its rating. The circuit is broken and the appliance is disconnected from the live supply.
A circuit breaker does the same job. It is a switch that trips when the current is too large, breaking the circuit. It works faster than a fuse and can be reset afterwards.