Depth of Field means how much of the image is in focus. A shallow d.o.f is when only a small amount of the photograph is in focus, and a deep d.o.f is when a large amount/all of the image is in focus. Depth of field is controlled via the aperture...the higher the aperture, the narrower the depth of field.
A camera can only focus its lens on a single point, but there will be an area that stretches behind and in front of this point that will still appear in focus. This zone is known as the 'depth of field'. It's not a fixed distance as it can change in size and can be described as 'shallow' where only a small amount of the picture is in focus, and 'deep' where a lot of the image is in focus.
The diagram below shows the differences between the various depth of field types.
My Experimentation
This gallery is my experimentation with depth of field.