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.
This means it must be connected using wires thick enough to carry 4 amps comfortably. Often the power consumption of a component will be stated in watts, which are found by multiplying amps and volts. The lamp in the example consumes 48 watts.
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.
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.