Simply put depth of field (DOF) is how much of the photograph in front of and behind the main subject that is in focus.
This however is not an even distribution. The range is approximately 1/3 in front of the main subject and 2/3 behind it.
To maximize your DOF do not focus right on your main subject. Focus 1/3 of the distance into the scene with the lens aperture set to the smallest possible.
The part most people have difficulty with is how do you change the depth of field and why would you want to?