The evaporator coil.

The evaporator coil is the indoor coil, usually shaped like a steep A or a slab sitting above the blower in the air handler. Cold liquid refrigerant enters it, boils off as it absorbs heat from the air moving across it, and leaves as a gas.

That boiling is the whole trick. Evaporation is what carries the heat out of your house.

It is also a dehumidifier

The coil surface runs below the dew point of the air crossing it, so moisture condenses on it and runs off into the drain pan. That is why an air conditioner produces water, and why the drain line matters as much as anything electrical.

In dry Phoenix air it produces less than it would in Houston, but five months of running still puts a great deal of water through that pan.

Why it freezes

Two causes, and the drawing on the frozen coil guide shows where to look.

Airflow. Not enough air across the coil and the surface drops below freezing. Filter, blower wheel, closed vents, crushed duct.

Charge. Low refrigerant means low pressure, which means a colder coil. If it is low, it leaked, and the leak is the actual job.

Once frost closes the fins, less air gets through, which makes it colder still. It compounds until the thing is a block of ice.

Cleaning one is a different job

An outdoor coil can be cleaned in place in half an hour. An indoor coil is inside a sealed cabinet, often in an attic, frequently with the drain pan and sometimes the refrigerant lines in the way. It is a considerably larger job, and a badly fouled one can land past the one thousand dollar ceiling that applies here.

Keeping a filter in it is most of the prevention. A coil only gets dirty if something is letting dirt reach it.