Depth of field refers to the part of the image, from foreground to background, that is in focus. A shallow depth of field, mostly used in portraiture and macro photography, shows only a small portion in focus. Aperture plays a big role in depth of field. Larger apertures produce relatively shallow depth of field. Smaller apertures produce greater depth of field. The image below is a good example of depth of field where near and far items are out of focus while the middle is sharp.
Also see: Aperture.