When an electrical component stops working the fault may be in the component, in the electrical circuit or in the fuse that protects them. Because the fuse is a likely cause, and the easiest to check, look at it first.
A headlamp bulb, for example, is designed to have a degree of resistance so that it consumes a certain current to glow normally. But there are at least two headlamps in the circuit. If they were connected in series, electric current would have to go through one headlamp to get to the other.
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.
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.