Since this site is known as f8pix, thought the very first photography article should handle the basics of the f stop. Very briefly, the lower the f number, the wider the aperture is open. Glance at the img to see what I mean.
So, what exactly does this mean to you? Well, as you can guess, the lower the f-stop (wider the aperture) the more light comes in. So, if you're looking for more light to get the proper exposure, adjust the f-stop to a lower setting.
However, there are impacts besides the light and exposure. A low f-stop creates a shallow depth of focus. This means that with an f-stop of say, 2.8, you could focus on a subject, and everything else in the picture would be out of focus and blurry. Why the heck would you want that? Actually, it's very common, especially in portrait photography. You often only want your subject in focus with the background blurred. That draws the eye to your subject, makes the subject stand out and gets rid of any distracting details that might have been in the background.
Take a look at this picture, this is taken with an f-stop of 2.8, as you can see the branches behind her and the tree to her left are significantly out of focus making them all far less distracting. If they were all in focus she just wouldn't stand out nearly as well as she does.
On the other hand, if you were shooting something that you wanted to be 100% in focus, you'd do the opposite, go with a high f-stop. If you have a point & shoot camera with settings for portrait, scenery, etc, your camera is making these adjustments without you having to know exactly what an f-stop is. But, isn't it more interesting to know? So, a portrait setting on a point & shoot camera should be giving you low f-stop (wide aperture), and a scenery setting the opposite.
There are other factors that contribute to the focus, though. A high zoom with a low f-stop will make the depth of focus even shallower than a low f-stop with a wide angle lens. So, the background blur effect will change dramatically with the same f-stop if you are wide angle, say 28mm, vs zoom at 300mm. The 300mm zoom with an f-stop of 2.8 will have an extremely shallow depth of field.... but wait, it does also depend on the distance to your subject. Oh no!
It depends on the relative distance between the subject and the foreground/background objects you expect to be blurry. If your subject is 15ft away, and the background is a mountain 20 miles away, you can bet the mountain will be very blurry as the distance ratio is so great between the two. But, if your subject is 15ft away, standing in front of a wall that is only another 1 ft behind them, the distance ratio is small, so there will be a very minor blur. Move them another 15ft in front of the wall, and the wall will become much more out of focus.
If you look at the picture above, the tree is about 3 times further away than she is, so it's significantly out of focus. If she were standing right next to it, it would be far more distracting.
That takes care of the f stop basics, more or less. Basically, the f-stop can be used to control both light and depth of focus. Something to keep in mind and experiment with.