Exposure

Basically exposure is a measure of the amount of light let into the camera while taking a picture. The idea behind exposure is to control how a subject appears, which for artistic purposes may be lighter or darker than the average light of the scene. The term overexposure is used when all detail is washed out of light areas, and underexposure used when all detail is lost from dark areas. On an automatic exposure setting the camera matches the average tone of the scene and adjusts the exposure for you.

Sometimes, however, you want an image to be over or underexposed. Then you switch to manual controls and use the shutter speed and lens aperture to create the exposure you want. The shutter is a thin sheet covering the light sensitive portion of the camera. When it opens it allows light in, allowing the picture to be taken. Shutter speed is the measure of how long the shutter is open and is measured in fractions of a second so the lower the shutter speed the more light is let in. Slow speeds introduce blur, while fast ones reduce it, but may not let enough light in. Lens aperture is similar: it is the opening in the camera lens that regulates how much light is let in during the time the shutter is open. The measurement is called an f-stop, and the smaller the f number the larger the opening. Generally a low f-stop requires a high shutter speed.

On my camera, a Canon PowerShot SX110 IS, there is a manual mode that allows me to control both the lens aperture and shutter speed. Additionally there is an aperture priority mode and a shutter speed priority mode that allows me to control that aspect while automatically selecting the opposite element.

References here, here and here.