Depth of field can be used to enhance or draw focus to certain aspects of your photo.  Bokeh, which is Japanese for blur, is a technique where the foreground is in focus, and the background is not.  You can achieve this effect by setting your camera to a wide aperture.  An out of focus foreground can be useful when photographing something behind a fence, or something similar.  Moving close to the fence and using a aperture just wide enough to blur the fence, will focus on the background.  A shallow depth of field is used for macro photography.  

Bokeh

Out of focus foreground

Close up