When you focus a lens on an object you will have a certain area in front of and behind it which are in focus; beyond the boundaries of that area everything will become progressively blurry. This effect is present in our own vision as well...the easiest way to see this is to hold your hand up in front of your face and focus your eyes on it; notice how the background is blurry while your hand is in focus, and vice versa. That is depth of field.
Shallow Depth of Field means that only a small area of your image(near your focal point) is in focus. The following illustrations show the same scene with two different focal points:
As you can see, when the person closer to the camera is in focus, the one in the background is blurry. However, when the man farthur back is in focus, both the woman close up and the building in the background are blurry, because shallow depth of field affects the image both in front of and behind the focal point.
Wide Depth of Field results in much more of your image being in focus. This illustration shows very wide depth of field; everything on screen is equally sharp, regardless of it's distance from the camera.
There are two primary factors which affect depth of field when working with video:
The first is the aperture setting;the wider open your iris is, the shallower your depth of field. Thus, if you want everything in focus, you need to have your iris(exposure control) turned way down, which in turn means your subject needs to have a lot of light on it. Likewise, if you want very shallow depth of field you need to open the iris up wide; this means you need to find another way to reduce the light in the scene, either using ND filters or less lights.
The second factor is the size of the CCD's in your camera. In general, the smaller the chips, the greater the depth of field. This means most consumer/prosumer cameras, which use very small chips, will have very wide depth of field. This is one of the key image qualities which seperate film and video. Because 35mm film is much larger than most CCDs, filmed images usually have much shorter depth of field...thus, if you are trying to mimic the look of film on your video camera, do whatever you can to reduce the depth of field(more on this in a couple of weeks).
Using a shallow depth of field allows you to focus your audience's attention on a particular element of your scene. A common effect is to combine shallow depth of field with a focal point that changes over time, thereby guiding the audience's attention from one subject to another. This effect is called rack focus.
Rack Focus is frequently seen in feature films, and it can be a powerful effect when used carefully. However, it is very difficult to achieve with a consumer video camera. This is because of the generally wider depth of field and the electronic focus systems used on consumer cameras, which simply aren't precise enough to work well for this effect.