Camera lens f-stops are the sizes of the hole through which light travels on its way to the film or digital sensor, and are typically adjustable to standardized sizes. The size of the hole determines how much light reaches the imaging plane (film or digital sensor) during exposure, and are used in combination with shutter speed and ISO to control the exposure of the image.
F-stops are generally written as f/n, where n is the f-stop number, for example: f/5.6. The f-stop number is the result of a mathematical calculation which divides the focal length of the lens, by the diameter of the entrance pupil (the size of the aperture). For example, if you have a lens with a focal length of 400 mm, and the entrance pupil diameter is 100 mm, the lens would have an f-number of 4. It would be referred to as an f/4 lens.
An f-stop with a larger number has a smaller aperture opening, and conversely, an f-stop with a smaller number has a larger opening. To illustrate this, refer again to the mathematical formula: 200 mm focal length, divided by 50 mm entrance pupil, equals f/4. Yet a lens of the same focal length, but with a larger entrance pupil of 100 mm, would be an f/2 lens. Thus, f/2 has a larger opening than f/4.
Standardized f-stops are usually adjustable in full stops, one-half stops, and sometimes one-third stops (for digital cameras, the available f-stop divisions can usually be set in the camera options menu).
Some typical full-stop f-stops are: f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32, f/45, f/64
Each full stop either halves the amount of light, or doubles it. For example, f/4 lets in twice as much light as f/5.6, and half as much light as f/2.8.
The size of the hole is usually controlled by a diaphragm blades inside of the lens, either manually, or automatically. The size may change statically, while being manually adjusted, automatically at the time of pressing the shutter button, or while pressing a depth of field preview button on the camera body.
The aperture f-stop, aside from controlling the amount of light passing through the lens, also affects the depth of field of the resulting image. All else being equal, a smaller aperture (higher f-number) has more depth of field than a larger aperture (lower f-number). This is a result of how the light rays pass through the different size aperture hole and are recorded by the imaging plane.