This is about photo cameras, but not digital ones. It may work the same in digital cameras (especially the ones with exchangable lenses), but I'm not sure about that.

First let's talk about aperture. The aperture of a lens is the diameter of the lens opening. Sort of. Aperture is indicated by a number. The lower the number, the more light can enter the lens, so the shorter the exposure time can be. Typical numbers for apertures are: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, and higher. Mathematically inclined types (geeks) might see a square root of 2 pattern here, and that is no coincidence. Aperture 5.6 lets twice the amount of light through the lense compared to aperture 8. Something to do with diameter and area, I guess.
Anyhow, you would think that the more light the better (the perpetual problem with photography is that there is never enough light), so why have all these different apertures? Well, as always, there's a trade off. A bigger aperture (lower number) lets more light through, but limits the depth of field. This means that the distance over which objects will be in focus, will be limited. A small aperture (high number) will result in objects close to the lens being in focus, as well as object farther away from the lens. Often you want this. A big aperture (low number) will result in the object that you are focusing on being in focus, and then some objects close to that as well. Sometimes you want this. For example, when taking portrait pictures, you want the face of the person to be in focus, but not the wallpaper on the wall behind her. So far so good.

In the old days, when taking pictures (with Single Lens Reflex cameras, that is), you would look through the viewfinder (an thus through the lens), and you would see the depth of field, since you had manually selected the aperture. In other words, when you were composing the picture, you had the same aperture as when you would press the shutter button.
Not so in modern, electronic cameras. So, sometimes these modern cameras include a depth of filed preview button. Pressing this button closes the aperture to the value that you or the camera have selected, so that you can see what the depth of field will be. But why? Why not have the same aperture during composition as during exposure?

Well, it isn't just you looking through the lens. It's also the camera itself. Modern auto-focusing cameras have all kinds of sensors that also peer through the lens. This in order to be able to do the autofocusing. Since most autofocusing SLRs use passive autofocusing (can't focus in the dark), the sensors need as much light as they can get. Most cameras have autofocus assist lights as well, in case it is too dark for them to focus. Anyway, bottom line is that the sensors need all that light, so therefore the lens is wide open until you press the button. Kind of obvious, once you realize it, but try to find that explained in a book on photography. I never realized it until I read The Camera by Ansel Adams. Oh well.

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