I have written posts before on what depth of field is and what all the numbers mean. You can check that out here. That is not what this post is about. This post is showing practicality and application.
Depth of Field can be used to isolate your subject and make it very clear what it is you are photographing. Take the above two images as an example. The right image was show at f16 giving the image depth. Often times this is good for landscape images but in this case it cluttered up everything. Now consider the image on the left. It was shot at f2.8 giving a very shallow depth of field. This blurred the background and brought emphasis to the image I had in mind.
When you are out consider playing around with different f-stops just to see what it does to your subject.