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.
Electricity flows from a battery in one direction only, and some components work only if the flow through them is in the correct direction. This acceptance of a one-way flow is called polarity. On most cars the negative () battery terminal is earthed and the positive (+) one feeds the electrical system.
The sudden surge of high current in a short circuit makes the fuse wire melt, or blow, breaking the circuit. When this happens, see if there is a short circuit or a disconnection, then install a new fuse of the correct amperage rating (See Checking and replacing fuses).
The side and tail lights, however, which you may need to leave on when the car is parked, are always wired independently of the ignition switch. When fitting extra accessories, such as a rear window heater which consumes a heavy current, always wire it through the ignition switch.