I live in New Mexico. A swamp cooler is another name for an evaporative cooling system. They work best when the outdoor humidity is low.
Here is how I would describe the set-up to my child. A big fan is surrounded by excelsior pads on four sides. They are fixed so they do not get caught in the fan by a vented metal box. Our box is the size of a washing machine, and is on our roof. A small water hose gets the excelsior pads wet. The one at our house takes four minutes to get the pads all the way wet. Then the fan turns on and air from outside passes through the wet excelsior through the vent in our ceiling. We feel cooler because the moisture evaporates off of our skin in a hurry.
That is the extremely non-technical explanation, and may have an incorrect detail. I hope it is enough to give you the idea of a swamp cooler.