LESS air. It's a valve (butterfly valves, like one the ones that open and close on giant superchargers mounted on drag race cars) that leaks when it's closed; on most carbs, either there is a valve that only controls the amount of fuel/air mix, but doesn't close all the way unless the choke is activated, or there is a completely separate choke valve that is closed when the choke is applied.
The airflow is significantly reduced, and like putting your...hand...over the end of a vacuum cleaner hose, any other openings that are present (like leaks in a vacuum cleaner hose) increase their flow to help offset the low pressure. Inside a carb, this usually includes the fuel atomizer (where the venturi is- a venturi sounds much more technical than it is; it's basically just a part of the air passage which has been narrowed in a mathematically designed way). More suction results from the lower volume of air being allowed into the motor, which draws more fuel out of the atomizer.
The other stuff, such as the idle speed adjustors, are secondary mechanisms that are turned on at the same time as the choke to make it more effective/prevent stalling. They are not the same mechanisms, but linked. It's a similar setup to acceleration pumps: on large car carburators, when you stomp the throttle there is a little piston that also jumps; it blasts a bunch of fuel into the carb to cover the slack as the normal jets are still adjusting to the instant change in fuel demand caused by you opening the butterfly valves in a hurry. Secondary fuel jets are often used to help with the choke, too. They work in concert with the throttle, but are not actually the throttle. The idle adjustors and secondary jets work in concert with the choke if they are designed to, but are not actually the choke.
Best high school class ever: Small engine repair
EDIT: More about venturis- imagine the top of an airplane wing. The low pressure area at the top of the wing is responsible for a lot of the lift, drawing the wing up into the low pressure area. A venturi is basically the same idea, but in a circle with the wing wrapped up like a ring with the top facing in. In the middle of the circle of low pressure is the fuel jet/atomizer- instead of drawing a wing up to provide lift, it draws gas out to provide fuel.