DOF refers to how much a photograph appears to be in focus. If the main subject is in focus, but the foreground or background is blurred, the photo is said to have a shallow DOF. If most all of the photo is in focus, including the foreground and background, the photo is said to have a deep DOF. It is determined by the distance between the camera and the subject, as well as the aperture (aka f-stop) and focal length of the lens.
Distance: Moving the camera closer to your subject can cause blurring in the background and foreground of the picture, producing a shallow DOF. Moving away from your subject has the opposite effect; the entire picture comes into focus, providing a deep DOF.
Aperture: Different f-stop settings for aperture provide varying degrees of blur. A wide aperture (indicated by a low f-stop number) provides a shallow DOF, resulting in the main subject being in focus and the foreground/background being blurred; it is useful when taking portraits or when using a macro lens and brings more attention to your subject. A narrow aperture (indicated by a higher f-stop number) provides a deep DOF and results in the entire photo appearing in focus; it is useful when taking landscape or wide-angle photographs.
Focal Length: The focal length of a lens also can appear to have an effect on DOF. A wide-angle lens with a short focal length tends to produce a deep DOF, making most of the picture appear to be more in focus. A telephoto lens with a long focal length tends to produce a shallow DOF because of the narrow angle of view and increased magnification - less of the background can be seen and any portion of the background that is already out of focus is magnified. A 200mm lens at 20 feet from your subject will show a very shallow DOF compared to a 50mm lens at the same 20 feet distance; of course, to maintain the size of your subject in the frame, you would need to adjust your distance.
IMPORTANT: The amount of DOF can vary significantly depending on the sensor size of the camera. Most compact point-and-shoot cameras have very small sensors and cannot achieve a shallow DOF.
NOTE: The type of blur mentioned in this solution is not related to blur caused by subject movement.