Depth of Field refers to the zone of acceptable sharpness in a given picture. A large, or deep, depth of field means that items in the foreground and background of a picture tend to be in focus. A small, or shallow, depth of field means that only one small part (such as your main subject) tends to be in focus, while the foreground and background tend to be out of focus. The depth of field correlates to the f-stop number in your camera settings. f/1.4 would be a shallow depth of field, while f/32 would be a deep depth of field. The smaller the f-number, the larger the aperture opens for that given shot.
If you want to isolate your subject, such as taking a picture of a person in front of a background that does not add to the picture, try using a large aperture (small f-number). Now, focus on your subject and take the shot. This will produce, in most cases, a very pleasing picture with a slightly blurred background. If you are taking landscape photography, and want the whole scene in focus, try using a small aperture (big f-number). This tends to give the best results, keeping everything in the shot in focus. Keep in mind that as the aperture gets smaller (bigger f-number) the slower the speed of the exposure will need to be.