When a certain amount of current being drawn from a plug socket is exceeded, the fuse is designed to blow to protect the wiring in the house and the appliances connected to that specific circuit. Electricians install fuses as a safety feature so that a large surge in power does not cause an electrical fire. A fuse is simply a small wire running from one electrode to another electrode and encapsulated in some kind of fire-proof casing.
An appliance that needs more power than a fuse can supply will ultimately blow the fuse. Most houses use circuit breakers that operate by similar means. If too many appliances trying to draw power from a wiring system at once, switching on a new appliance can trip the circuit breaker and cut power, which is why switching on an appliance such as a light can cut the power in a house.