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It's fairly simple. Say you're so lazy or don't have the time to focus precisely for every shot, you can instead set the lens to focus at an approximate distance and given a narrow enough aperture (smaller f/ number) you can get acceptable sharpness over a certain range (near to far).
Say you're some gimp that shoots "street portraits" and the people are typically around 2m away, you can focus the lens at 2m and stop down to say f/8 and using the depth of field scale on the lens see that you'll have objects from say 1 to 4m in focus. Or if you have a wider lens and stop down more you can perhaps get 1m to infinity in focus, and then you know that both your subject and anything in the background will be in focus.
