Hi There:
Welcome to the list... There are a number of threads here already on different cameras; you might want to do a quick search and see what you come up with.
In really simple terms... let's see. Photography is all about light. Light enters through the lens and strikes either a piece of film coated with chemicals that are sensitive to light, or an electronic sensor that measures and records the light. There are three ways to control the amount of light reaching the film or sensor. One is to control the amount of time the film or sensor is exposed to the light - the shutter speed. The second is the sensitivity of the film or by mimicking that electronically - called ISO after the international standards association. Most films have a given sensitivity, with electronic cameras you can adjust the sensitivity and trade off higher sensitivity for more electronic noise.
The third way to limit the amount of light reaching the film or sensor is to have a diaphragm within the lens that opens and closes. These are your f/stops. Now every f/stop lets in twice as much light or half as much light as the f/stops on either side of it.
So let's assume that we start with an f/stop value of 1. If we double that we get 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2049, 4096, 8192 and so on. The numbers get big really fast. So rather than using absolute numbers it was decided to use the square roots. Therefore you have 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, etc. Remember that the bigger the number, the smaller the lens opening. These numbers would be more correctly written as 1, 1/1.4, 1/2, 1/2.8, etc. as the numbers represent the square roots and each one lets in half as much light.
The actual value of the maximum f/stop depends on the lens diameter, focal length, etc. Therefore some lenses have a maximum opening of f/3.5 or f/1.7 or something like that. In the old days f/stops were controlled manually by clicking a dial that opened and closed the diaphragm and so the numbers were pretty much fixed, as were the shutter speeds. With electronic controls things get a little less fixed. The trade-off between f/stops is that a greater lens opening yields less depth of field. A really small f/stop like f/22 can create its own problems. Entire chapters have been written on this, so this really only begins to skim the surface.
Mike.