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).
To guard against this, ancillary circuits have fuses. The most common type of fuse is a short length of thin wire enclosed in a heatproof casing often glass. The size of the fuse wire is the thinnest that can carry the normal current of the circuit without overheating, and it is rated in amps.
Thin wires conduct less easily than thick ones, because there is less room for the electrons to travel through. The energy needed to push current through a resistance is transformed into heat. This can be useful, for example in the very thin filament of a light bulb, which glows white hot.
If the wrong-sized wire is used, or if a wire becomes broken or disconnected, this can cause an accidental short circuit which bypasses the resistance of the component. The current in the wire may become dangerously high and melt the wire or cause a fire.