If the cable overheated, there could be a fire. The fuse prevents that happening, because its thin wire will melt and break the circuit long before the cable itself can heat up and burn. Some cars have only two fuses. One rated at about 30-50 amps protects components wired through the ignition switch — flashers, wipers, heater-motor and instruments.
Depending on the fuse design, it is sometimes possible to tell whether it has blown by holding it up against a light; a break in the wire inside may be visible. Another clue is blackening of the glass cover. If there is no visible sign, check by fitting another fuse of the same rating; if that cures the trouble, then the fuse was to blame.
All the electrical units of measurement are interrelated: a pressure of 1 volt causes a current of 1 amp to flow through a resistance of 1 ohm. Volts divided by ohms equal amps. For example, a light bulb with a resistance of 3 ohms, in a 12 volt system, consumes 4 amps.
The electrical system of a car is a closed circuit with an independent power source the battery. It operates on a small fraction of the power of a household circuit.