The ƒ-number is an expression of how wide open the aperture of the lens is. I
think an aperture of 1.0 means the iris is completely open, while ƒ/16 is very small. I forget the progression, but each higher number represents a halving of the open area of the iris. Aperture and shutter speed are directly linked in that they control how much light reaches the sensor. At a given aperture/shutter speed pair, if you open the aperture one stop you send more light to the sensor. If instead you slow the shutter speed, you *also* send more light to the sensor. It's a balancing act. The other thing you impact with the aperture is the depth of field. For example, this picture of Josh's duck was taken with the aperture wide open:
(click for bigger)
Note how the duck (which is what the camera's focussed on) is sharp, but the background is blurry. If instead I'd taken the shot with the aperture at ƒ/16, the background would also be sharp. But to expose the scene properly you'd also have to decrease the shutter speed.
