You place things in a desiccator to dry them (or to keep them dry). It is in effect an air-tight and chemical resistant container which has two compartments, one at the bottom which holds the drying agent (or desiccant) and above this a shelf where you can put beakers or small trays with the solids you want to dry. It is most often made of thick, vacuum-safe glass so that it can be evacuated without any risk of implosion.
The idea is to keep a substance away from any moist air and close to a drying agent (but not in contact with it!), another substance which absorbs water much more strongly than the compound you wish to dry (left overnight, most traces of water will travel from your compound and become absorbed by the desiccant). Concentrated sulfuric acid, sodium or potassium hydroxide pellets or flakes, phosphorous pentoxide or anhydrous calcium chloride all make good drying agents for most substances. Always use an acidic drying agent for acidic substances and a basic one for bases, otherwise salts may form between their vapors.
If you evacuate the desiccator, the process is more rapid, as water vapor evaporates from your moist compound much faster under vacuum, as it is only when it is in form of vapor it will be absorbed by the desiccant. Vacuum is optional though, if your compound does not bind water very strongly. In rare cases it may even be necessary to heat the desiccator to 100°C under vacuum to driuve all the water out, but that is most often only necessary for analytical work.