When the engine is cold a richer fuel mixture is needed. As it warms up the mixture must be leaned out. This is where the automatic choke circuit comes into play.
Choke Thermostatic Coil
The choke shaft extends through the carburetor into a round housing. Inside the housing there is a thermostatic coil spring. This spring will wind & unwind depending on the temperature. When cold the thermostat will hold the choke valve closed. As the temperature warms up, the spring expands and allows the choke valve to open.
The choke vacuum piston is linked to the choke butterfly by a small linkage. At idle, which will have full vacuum, the piston will be pulled into the piston well. This puts pressure against the thermostat coil trying to open the choke valve slightly.
Not all carburetors will have this air valve. Marvel Schebler & the Holley 1 barrel carburetors are a few examples that do. The air valve is placed offset on the choke valve. This keeps the choke from causing a too rich condition.
Most automatic chokes systems will use a stove pipe to heat up the thermostat coil. The pipe heats up, using the exhaust manifold and the heat is then pulled up to the thermostat using vacuum from the carburetor, which is fed by the intake manifold.