Compressed air can't hold as much water vapour as atmospheric air of the same temperature. Hot air also has the ability to hold more water than cold air. Its a little bit like dissolving salt in water. You can only dissolve just so much salt into a pint of cold water, but you can dissolve a lot more salt into boiling water. However, when the boiling water finally cools down, the dissolved salt will come out of solution and crystallise.
Air acts in the same way.
Air is cooled down and the temperature at which condensation begins is measured. The actual water content of the air is then obtained from a set of steam tables. These air direct reading devices which usually measure the change in dimensions of a material due to the amount of moisture it contains. Older hygrometers used wood or paper and the changes in dimensions due to humidity would take ages to stabilise. However, depending upon the size of the system it may take another day to finally stabilise.