If the battery voltage drops, less current flows, and eventually there is not enough to make the components work. The extent to which a wire resists the flow of current is called resistance, and is measured in ohms.
If the wrong-sized wire is used, or if a wire becomes broken or disconnected, this can cause an accidental short circuit which bypasses the resistance of the component. The current in the wire may become dangerously high and melt the wire or cause a fire.
Often, however, it is hidden away, perhaps under the dashboard or down in the front knee-well. The car handbook usually gives the location, but without a book finding the box can prove difficult. Get to know where it is before anything goes wrong.
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.