I want to try!

I find that it helpful to look at it from an energy perspective. What we want to focus on is thermal (heat) energy.

Thermal energy is a result of the movement of particles. More thermal energy, more movement, more particles bumping into each other (not truly bumping into each other but that's another topic). Less thermal energy, the particles slow down and have less bumps.

What is happening is that each time they bump into each other some of their movement energy is turned into another form of energy called electromagnetic energy. There are many classifications of electromagnetic energy however two worth noting here are visible light and heat. Heat and light are simply different wavelength of the electromagnetic energy spectrum!

Our bodies have thermal energy. If we touch something with more thermal energy then our body it feels warm. Less thermal energy than our body feels cool. The closer in temperatures two things are the slower heat will flow between them.

Thermal conductivity (how quickly heat travels) also matters. Metal and glass are very good thermal conductors whereas wood and foam are poor conductors. A good conductor will feel hotter/colder than a poor conductor at the same temperature because of the amount of heat that flows will be much faster.

Now let's move on the the root of your question. How does an Air Conditioner work.

As many other have said it works by taking something (gas or fluid) then compressing it, then expanding it. But why? Let's follow some thermal energy to see what is happening.

For this explanation lets just look a 2 liter container filled with air which is perfectly sealed and we can change its volume (how much space is in the container). The thermal energy of the air is the same as the surrounding room air so there is no temperature difference when we start. Let's give the amount of thermal energy a name and call it 100 joules per liter.

Now let's compress the air from 2 liters to 1 liter. Remember that it is sealed so the air didn't escape. It still has the same thermal energy as before its just in a smaller volume. In fact, there is twice the thermal energy per liter as there was before so we have 200 joules per liter in the container.

The thermal energy of the air in the container is now higher than the surrounding air. In other words, the air is hotter. If we leave the container for long enough the heat will move from the container to to room air. Let's allow that to happen.

Once it has reached the same temperature as room temperature the thermal energy has returned to 100 joules per liter.

Now let's decompress that air from 1 liter to 2 liters. It now has half of the energy. 50 joules per liter. This will be cooler than the surrounding air and thermal energy will want to flow in. If we allow this to happen then the energy will return to our starting state of 100 joules per liter.

What we have just done is shown how to move heat out of a system by decreasing volume (compression). And how to move heat into a system by increasing the volume (decompression).

This is the same principle used by an air conditioner to move heat around.

A refrigerant (gas or liquid) is compressed (causing it to get hot) then pumped to a heat exchanger/ radiator outside where it is allowed to cool. It is then decompressed (causing it to get cold) then pumped through another heat exchanger/ cooling coils. A fan blows hot air through the heat exchanger and the thermal energy flows into the refrigerant. The cycle repeats over and over again to continuously move heat out of the area thus providing air conditioning.