A kind of atomizer operated by compressed air and used for spraying on paint or another liquid.

Hey, that's just plain rude. An airbrush not only amounts to, but IS a personal tool.

The basic principle is that a compressed gas or plain air flows through the airbrush and sucks up paint with it, depositing the paint on a surface. If you don't need precision, this is done externally i.e. a can of paint is placed before the outlet of the airbrush, and the flow of air sucks up the paint with it and deposits it on the surface of choice.

This type of airbrush is most often used to paint large surfaces rather than details and are thus designed only to distribute paint in the most even fashoin to a surface - be it a boat, a car or a scale model.
However, if you need a more precise painting tool (for modelling purposes) and still want to avoid those nasty pencil streaks you get when using a paintbrush, you need an internally mixing airbrush. This airbrush mixes the paint internally (hence the name) and uses a fine needle to direct the paint flow so you're able to attain sub-millimetre lines with this fine painting tool - they're available in two flavors (not counting the cheap plastic variants):
Single action: this airbrush lets you control the air flow with a button on the top and you have to adjust the paint flow with a screw on the back. It all becomes very clear once you've bought your first single-action airbrush.

Double action: by moving the aforementioned button on the top of the airbrush back- and forwards you basically adjust the paint flow - this is pretty cool since once you've figured out the line width of the airbrushing you want to do, you can just press the button a bit backwards to be able to paint faster and still deposit the same amount of paint - as always it takes a lot of practice to become proficient in this discipline, but trust me - it's well worth it.
An airbrush can be used to apply inks, different types of paints and lacquers to a surface AFAIK in an even way and various techniques can make it possible to do it in a way that no paintbrush can.
The all important thing here is to keep the airbrush moving in order to avoid the paint running and to wear a mask at all times and / or have proper ventilation as an airbrush is the mother of all kinds of weird particles getting into your airways.

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