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.
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.
The strength of the current is measured in amperes (amps); the pressure that drives it round the circuit is called voltage (volts). Modern cars have a 12 volt battery. Its capacity is measured in amp/hours. A 56 amp/hour battery should be able to deliver a current of 1 amp for 56 hours, or 2 amps for 28 hours.