How does a fuse protect the electric wiring (or an appliance) from being damaged?

During short circuiting or voltage fluctuations maximum current passes through the wires causing burning of the wires. To prevent this damage a fuse is connected to live wire of the circuit. When there is a short circuit, the fuse wire gets heated up to the extent that it melts. As a result, a gap is produced in the live wire and the circuit breaks. No current then flows and electrical appliance or circuit is protected from being damaged.