The illuminating power of a lens is a function of the focal length of the lens and the diameter of the aperture ( iris ) through which the light is allowed to pass.
The amount of light falling on a film or electronic sensor can be adjusted by changing the diameter of the aperture; but instead of recording the actual diameter, we can treat all lenses equivalently if we record the aperture diameter as a function of the focal length.
Thus we record apertures as f/n (focal length divided by a number n). e.g. a 50mm lens at f/2 has an aperture of 25mm, an 80mm lens at f/2 has an aperture of 40mm, but both have the same illuminating power.
A standard series of apertures has evolved such that the illumination doubles or halves with each click-stop (f-stop). If you double the diameter (or radius) of a circle, you quadruple the area (area = πrČ), and it is the area which determines the level of illumination.
Thus, to get from one f-stop to the next, the number n is not doubled, but multiplied by the square root of 2 (= 1.414). The standard f-stop series thus comes out as 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, etc. i.e. the number doubles for every 2 steps in the series. The smaller the number n, the larger the aperture.