What is aperture?

The aperture is the variable opening of the camera lens and controls the amount of light that strikes the film or censor. Each variation is referred to as an f-stop.
Imagine the aperture of the lens is like a tap. The more you open a tap the more water pours through it. The more you open the lens aperture the more light pours through it. Remember, the shutter speed controls how long light is exposed to the film or censor, the aperture controls how much.

Like the shutter speed, each 'stop' is half or double the preceding one.

Common f -stops are:

f/2.8 f/4 f/5.6 f/8 f/11 f/16 f/22
<-- wider............narrower -->

Modern cameras may also have increments between the above f-stops.

The aperture is used to control depth of field (Dof). An in-depth explanation of Dof can be found here, but in a nut shell, the wider the aperture the narrower the Dof. And conversely the narrower the aperture the greater the Dof.

The iris of your eye behaves in the same way as the aperture of a camera lens. Generally, our eyes are about an f/8 in terms of Dof.

The aperture and shutter speed are used in conjunction to obtain a correct exposure. Usually you decide what you're going to photography and make the settings accordingly. For instance, if you're photographing motor sports, your primary thought will most likely be sharp images of vehicles so shutter speed will dictate your game. If you're photographing landscape type images then aperture will the controlling factor. Likewise, if you're hand holding the camera, you'll need to be conscious of shutter speed to prevent camera shake.