Electric fuses, in any application, are designed to fail when too much amperage runs through them. They are designed as a weak point to protect the rest of a given circuit from damage and fire, to and prevent electric shocks. Fuses blow by heating up and melting before the rest of the circuit does. This is accomplished by using a short piece of metal that is higher in resistance, or has a lower melting point, than the rest of the circuit.
Electric circuits are designed to carry a certain amount of voltage and amperage. The components of the circuit each provide a certain amount of electrical resistance. This resistance limits the amperage that can flow through the circuit. Electrical engineers size the wiring, components, and fuses to fit the needs of the circuit. If for some reason wires become exposed and contact one another or the car body, a short circuit is formed. This short bypasses all of the resistance of the components that was designed into the circuit and allows too much amperage to flow through the wires. The first thing to heat up and fail should be the fuse, eliminating many hazards. Were it not for the fuse, the wiring would continue to heat and cause fire and shock dangers.
Many mechanics dread automotive electrical work. The bundles of wires (wiring harness) running through a modern car is dauntingly complex. There can be hundreds of wires of all different colours and with different-coloured striping. Wiring diagrams label the colours of the wires, but it is easy to confuse the colours of the actual wires; especially if they have faded over time. Circuits in a car are made to run at different amperages. If two wires are accidentally switching during a repair, both circuits will suffer. For example, let's say that fuse "A" is a 5-amp fuse at the box, and fuse "B" is a 20-amp fuse at the box. The electric circuits in the harness require 5 amps for circuit "A" and 20 for circuit "B." If the two were incorrectly wired somewhere along the harness, fuse "A" would blow, and circuit "B" would be damaged from too many amps.
Simply putting the wrong fuse in a spot in a fuse panel can cause a fuse to blow. If your panel diagram calls for a 12.5-amp fuse, and you put a 10-amp fuse in because that's all you have, it may last a while, but it will blow eventually from too many amps and overheating.
Many aftermarket car parts require more power than their stock equivalents. This is particularly true for power inverters, stereos and lighting. In these cases the fuse will blow unless special wiring and fuses are installed to counteract the excess load.