In a negative (-) earth-return system, the current flows from the positive (+) terminal to the component being operated. The component is earthed to the car body, which is earthed to the negative (-) terminal of the battery.
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.
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.
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.