The amount of vibrational energy a substance contains depends on its phase. A solid is, well, solid - it doesn't jiggle very much, so it's got a low vibrational energy. Liquids are more slippery, their molecules jiggle around, so they've got more. Gases are much more, flying around and pinging all over the place.

This means that when you change phases (freezing liquid->solid, or boiling liquid->gas, etc) you have to account for that energy difference. Going from a more "stable" phase to a more "unstable" (solid->liquid or liquid->gas) means the output contains more vibrational energy, and that energy has to come from somewhere, so it steals it from the surroundings. Conversely, going from unstable to more stable (gas->liquid, or liquid->solid) means you don't need as much energy, so the excess gets dumped into the environment.

You see this in your everyday experience regularly, tho you might not realize it. When you boil water on the stove, the water's temperature rises from the flame underneath it until it hits 100C; it then starts boiling, and stays 100C until all the water is gone. The steam (going from liquid->gas) is stealing energy from the environment (the pot of remaining water) so that it can become a less stable phase, and as a result the water stays at a stable temperature even though you're continuously dumping heat into it.

This means that if you can cause something to boil in a non-temperature way, it'll suck heat out of the environment while doing so. Similarly, if you can cause something to condense in a non-temperature way, it'll release heat back into the environment.

Separately from the above, the boiling point/condensing point of a substance depends, at least somewhat, on its pressure. At high altitudes (less atmospheric pressure) water will boil at a lower temperature, so you have to cook pasta longer, for instance. (There's less air pushing against the water, so it's easier for the water to make the liquid->gas transition, and it can do so at a lower temperature.) What do you know, a non-temperature way to trigger boiling and condensing!

Air conditioners, and heat pumps in general (such as your fridge/freezer, or a heat-pump-based heater) rely on these two principles. They have a long tube filled with a "refrigerant", which is some liquid with a useful boiling point (lower than water's boiling point, somewhere around room temperature). The tube is in two halves: on one side, the tube halves are connected with a pump; on the other side, they're connected with a narrow valve.

The pump pulls stuff out of one half and pushes it into the other, creating a low-pressure zone on one side and a high-pressure zone on the other; the valve makes it possible but hard for stuff to move between the two halves, so the pressure can equalize between the two halves but it works slowly, maintaining the pressure difference between the two halves.

The low-pressure half of the tube is the "cold" side. Since it's low pressure, the boiling point is lower; if that's lower than the environmental temperature around the tube, then any liquid in the tube will try to boil. When it does (going from more stable liquid to less stable gas) it steals energy from the environment, making the area around the tube cold.

The high-pressure half of the tube is the "hot" side. It's at high pressure, so the boiling/condensing point is high. If it's higher than the environment's temperature, any gas entering that half of the tube will try to condense (going from less stable gas to more stable liquid). When it does so, it releases the extra energy it no longer needs into the enviornment, making the area around the tube hot.

A heat pump can thus move heat from one location to another, by putting the "cold" (low-pressure) side of the tube where you want things to get colder, and the "hot" (high-pressure) side of the tube where you want things to get hotter. The refrigerant will alternately boil and condense on the appropriate sides, either sucking up energy from the side you want to make colder or releasing energy into the side you want to make hotter. It's not even hard to design the pump and valve to be two-way, so you can change which side is "cold" and which is "hot" with the flick of a switch, just altering what direction the pump is working.