The way an AC works is that by condensing water, a surface is cooled. By blowing air through this cold surface, the room is cooled. Well, at least sort of. Let’s leave it with that explanation.

Now if you set it to dehumidify, it basically does exactly the same, but might aim for target humidity rather than target temperature.

Cold air can take less moisture, so depending on circumstances, temperature and humidity, it might get colder but the humidity actually goes up.