A fuel pump is a frequently (but not always) essential component on a car or other internal combustion engined device.
Many engines (older motorcycle engines in particular) do not require any fuel pump, requiring only gravity to feed fuel from the fuel tank through a line or hose to the engine. But in non-gravity feed designs, power has to be pumped from the fuel tank to the engine and delivered under low pressure to the carburetor or under high pressure to the fuel injection system.
Carbureted engines often use low-pressure mechanical pumps mounted outside the fuel tank. In contrast, fuel injected engines often use electric fuel pumps that are mounted inside the fuel tank (and some fuel injected engines have two fuel pumps:
One low pressure/high volume supply pump in the tank and one high pressure/low volume pump on or near the engine).