What is Great Depth of Field? In simple terms, it’s keeping as much of your scene as possible in sharp focus. Ideally, subjects close to your camera and subjects far from your camera will be equally sharp.
Because it allows the viewer to see all the details of the scene, it’s often used in landscape photography:

Notice how all the trees, even into the distant background appear sharp. This was shot at f/ 22.

Notice how all the details are sharp in this image of a clear cut forest; from the woodchips in the foreground to the sad-looking trees in the background. The treeline in the far distance appears softer due to atmospheric haze. This was shot at f/16 (I would have shot at f/22, but did not have a tripod at the time to allow for the slower shutter speed.)
To try a great depth of field shot, change your f-stop number to the highest number your camera will allow. **To find out how to change your aperture (what is aperture?) or f-stop number, check your manual! To really see the results of your aperture settings, fill your scene with objects of varying distances.
You can also use Great Depth of Field creatively to help add details and information to a scene. This is common in environmental portraits, where a good amount of details from the subject’s environment are included in sharp focus within the image.

Great Depth of Field in an Environmental Portrait allows the viewer to see details in the subject’s environment. In this case, the details of the historic farmhouse add context about the character in this portrait.
Finally, consider your Depth of Field when shooting group shoots. To ensure that ALL the people in your group appear in sharp focus, use a higher F/stop number. ( I usually start with F/8 and then check to make sure everyone is sharp. If not, go to f/11 and so on until you get the desired result.)

Notice how all the faces are sharp in this group photo, even though the people are spread relatively far apart. It was shot at f/11.
Wondering what effects the opposite of Great Depth of Field will have? Check out the last photo school post: Shallow Depth of Field.