Autolite 4 barrel as used on Ford smallblock, ca. 1967
Essentially a carburetor is a solution to the problem that fuel comes in liquid form and needs to end up as a vapor to be combusted. Generally a carburetor is bolted to the top or side of an intake manifold (depending on the type) and uses the air rushing into the engine to atomize gasoline released from a port or "jet." Different brands of carburetors accomplish this in several slightly different ways, but the concept is the same for all.
 Carb circuits
Carburetors encounter various problems through the course of operation such as temperature, transition of throttle, amount of throttle, etc. For this reason, they have more than one "circuit." A circuit is a method of adding gasoline to the rushing intake air so that it can be atomized.
 Idle circuit
When idling, a carburetor uses the idle circuit. This is most often metered by a needle valve which allows a small amount of fuel to pass into the bore of the carburetor from the fuel bowl under idle condition.
 Primary or main circuit
Next, a primary circuit using different sized jets (and sometimes vacuum actuated rods inside the jets) responds to increased fuel demand (in the form of intake flow velocity) with more fuel allowed into the carburetor bore.
 Secondary circuit
Under high-throttle conditions, some carburetors are equipped with a secondary circuit, which is essentially another set of throttle bores/venturis fed by a second set of jets (similar to the primary circuit) which allow even more air/fuel into the intake charge, or a power enrichment circuit (Holley uses a power valve, Carter/Edelbrock use step up springs, Rochester uses a power piston, for example) that senses engine vacuum to determine the need for additional air/fuel mixture. Some carbs use both a secondary side (4 barrel or staged 2 barrel) and a power enrichment circuit.
 Transition circuit
A transition circuit, often referred to as an "accelerator pump" squirts fuel into the rushing intake charge and is actuated by positive movement in the throttle. For example, when pressing the accelerator from 1/4 position to 3/4 position, the accelerator pump squirts an amount of fuel proportional to the amount of accelerator travel into the carburetor bore. This amount can be modified by accelerator pump cams as well as a number of other methods depending on the brand of carburetor. The accelerator pump is also used to add fuel for initial starting in many cases (as when "pumping" the gas on a cold motor). Many carbs also use a "transition slot" that works similar to the idle circuit except that the transition slot is activated at throttle setting greater than idle, but less than the main or power enrichment circuits. It contributes to the overall air/fuel ratio from the point of its actuation through WOT. Obviously, the contribution of air/fuel mixture decreases in percentage the more the throttle is opened.
Under cold conditions, a choke circuit can be used which increases the amount of fuel in the intake charge. This is a solution to the problem that gasoline does not atomize well when it is cold. This circuit is activated either manually or by a bimetal coil (aka "automatic choke"). The bimetal coil can be heated by the engine or by a small electrical heating element to release the choke as the engine warms up. Most chokes also have a fast idle feature to them to allow the engine to remain running without the operator having to use the throttle during warm up.
Again, the reason for every circuit that a carburetor has is to provide a suitable air/fuel ratio and amount of air/fuel for operational/environmental conditions.