The aperture is the physical opening of a lens that lets light pass through to reach the sensor or film. Measuring the aperture by itself is not very informative, however.
The amount of light reaching a camera’s sensor is dependent on aperture and focal length. Because of this, photographers do not refer to the actual aperture of a lens, but rather to a quantity taking into account aperture and focal length: the f-stop, sometimes called f-number.
The following simplified figure is an example to illustrate this:
On this image, we see that even though both lenses have a different diameter (aperture) and distance to the sensor (focal length), both illuminate the sensor in the same way. Thus, both lenses would have the same f-number. This schematic is oversimplified, but serves the purpose of explaining why different lenses can have similar f-numbers.
How F-stops are calculated
F-stops are calculated by dividing the aperture by the focal length. The amount of light passing through a lens with a focal length of 100mm and an aperture size of 50mm will be the same as for a lens with a focal length of 200 mm and an aperture of 100mm. In both cases, the ratio will be 1/2:
50 / 100 = 100 / 200 = 1 / 2
Such an f-stop will be noted f/2, f2, 1:2 or f-2 (all are equivalent).
When reducing the aperture area by a factor of 2 (half the light will pass through), the aperture diameter will be reduced b a factor of 1,4 (square root of 2). This is why f-stops increments (each halving the amount of light passing through) seem to have unusual values (note that those values are rounded):
Increasing numbers = decreasing aperture size
Remember that increasing numbers actually mean decreasing apertures, because an f-stop is a ratio. Each increment representing a halving of the aperture is called a “stop”, so reducing an f/2 aperture by two stops would require a setting of f/4.