Aperture and f-stop are two photographic terms for the same thing. Aperture, or f-stop, is the camera's setting that determines the width of the passageway for incoming light. Inside lenses, there are blades that form an opening. The position of these blades, and consequently the size of the opening, are determined by the camera's f-stop setting. The numeric f-stop setting and the size of the opening are inversely proportional. In other words, when the f-stop is a large number, the actual size of the opening is small. And vice-versa, when the f-stop is a small number, the opening is large. This setting has two affects on the photos you are taking:

Rate of exposure
The wider the opening (smaller f-stop number) the more light will come in to the camera to expose the film. This means the film will be exposed faster. So, to compensate for this faster rate of exposure, the shutter speed must be shorter. The opposite is also true: with a smaller opening (large f-stop number) less light will come in, and the rate of exposure will drop. With this slower rate of exposure, a longer shutter speed must be used. So, if you wish to use a fast shutter speed (perhaps to 'freeze' action) simply increase the rate of exposure (by opening up the aperture), and the shutter speed can be increased.

Depth of field
Depth of field refers to the area in a photograph that is in focus. Whenever a photo is taken, the camera is focused for a given distance (this is usually done by looking through the camera and focusing on the subject of the photograph). This causes everything seen through that lens that is the same distance away to be in focus. In reality, while there a given distance that is being focused on, there is a range of distances in focus. This range is the depth of field. For example, if you focus your camera's lens on an object that is 10ft away, everything in the 9ft - 11ft range may be in focus. The further away things are from the 10 foot mark (in either direction), the more out of focus and blurry they become.

Aperture is a means of changing this range of values. As the opening widens (smaller f-stop numbers) the depth of field shortens. The opposite is also true: with a smaller opening (large f-stop number) the depth of field increases. This extends to the point where a very tiny aperture can render nearly everything in focus, and a very large aperture could have almost no depth of field and only a single distance would appear focused.

F-stop values are traditionally incremented by stops. Each stop is a standard value that allows half as much light through as the previous stop and twice as much light as the next stop. It is possible with most cameras to use half stops, but some even allow smaller increments of the aperture than this.

For reference purposes, the chart below contains most "full" f-stop values and their corresponding diameters. With high end equipment, it is possible to get f-stop values with smaller diameters than f/1 and and larger diameters than f/32.

f-stop Diameter
f/1 50 mm
f/1.4 35.4 mm
f/2 25 mm
f/2.8 17.7 mm
f/4 12.5 mm
f/5.6 8.8 mm
f/8 6.3 mm
f/11 4.4 mm
f/16 3.1 mm
f/22 2.2 mm
f/32 1.6 mm