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.
Some ancillary components can be operated without the ignition turned on by turning the switch to the auxiliary position. A radio is usually wired through this switch, so that it can be played with the engine off.
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.
Most are wired through the ignition switch, so that they work only when the ignition is switched on. This prevents you accidentally leaving something switched on which might cause the battery to go flat.