The sudden surge of high current in a short circuit makes the fuse wire melt, or blow, breaking the circuit. When this happens, see if there is a short circuit or a disconnection, then install a new fuse of the correct amperage rating (See Checking and replacing fuses).
Most are wired through the ignition switch, so that they work only when the ignition is switched on. This prevents you accidentally leaving something switched on which might cause the battery to go flat.
Some ancillary components can be operated without the ignition turned on by turning the switch to the auxiliary position. A radio is usually wired through this switch, so that it can be played with the engine off.
There are many fuses, each protecting a small group of components, so that one blown fuse does not shut down the whole system. Many of the fuses are grouped together in a fuse box, but there may also be line fuses in the wiring.