The popularity of carburettors was due in part to their straightforward nature, with most consisting effectively of just five key parts - the main body, a float chamber, a fuel discharge nozzle, a 'venturi' and a throttle system.
When you crank a carburettor-equipped engine, the pressure drop created when a piston travels down the cylinder on the intake stroke causes air to be drawn into the carburettor's 'barrel' - an opening that runs through its body. As this air travels into the carburettor's barrel it must pass through the venturi, which contains the discharge nozzle.
The throttle, typically a butterfly valve behind the venturi, controls the engine speed by regulating the flow of air into the engine. With the throttle almost closed, little air - and thus little fuel - is drawn into the engine, and vice versa.
Maintaining the correct fuel pressure at the discharge nozzle is achieved by the use of a float chamber, which functions like the cistern on a toilet. It contains a float, typically brass or plastic, which rises as the chamber fills. When it reaches a level that will result in the correct pressure as the discharge nozzle, it cuts off the fuel supply - and opens it again when the level falls. If the pressure were too high, fuel could be forced into the venturi, upsetting the mixture.
Carburettors are also often equipped with a choke, which usually takes the form of a flap or a butterfly. When in use it restricts the flow of air through the carburettor, increasing the vacuum on the engine side of the venturi and resulting in more fuel being drawn out. This is used to help get the engine started when cold, when myriad factors - such as the temperature being so low as to stop most of the fuel vaporising - are working against it.
A properly maintained carburettor can prove a relatively accurate and straightforward method of delivering fuel - and you'll still find them in applications where simplicity and reliability are key, ranging from garden equipment to light aircraft. Otherwise, in most modern applications, they have been superseded by more accurate, self-adjusting electronic fuel injection systems.