The blower motor.

The blower motor turns the wheel that pushes air through your ducts. It is the one part of the system you can hear working from inside the house, and it runs whenever air is moving, in cooling and in heating both.

The wheel it turns is a drum with a lot of small curved blades, which is why people call it a squirrel cage. Those blades are the first place dust accumulates.

Blower problem or cooling problem

Worth separating, because they get confused constantly.

No air at the vents at all points at the blower: its capacitor, the motor itself, or the control board telling it to run.

Plenty of air, but it is not cold points somewhere else entirely: refrigerant, the compressor, the outdoor unit. The blower is doing its job.

Weak air everywhere is usually not the motor. It is a filter, a caked blower wheel, or duct. A motor that is failing tends to stop rather than gradually weaken.

How it fails

The capacitor that starts it goes first, far more often than the motor. That is a cheap part, and the price depends on whether the unit is in a closet or an attic.

A wheel caked with dust unbalances the motor and makes it work harder. That shows up as noise, then as a motor that runs hot and shuts itself off on thermal overload, then eventually as a motor that does not come back.

Modern variable speed motors fail differently and are a good deal more expensive, often past the one thousand dollar ceiling that applies here. If that is where yours lands, you get told plainly and handed on.