DOF is Depth of Field. My definition of it, which will probably be better defined by others is related to the amount of background which is in focus. A shallow DOF has the subject clearly in focus while the background is very much out of focus and blurred. A wider DOF is when both the foreground is in focus as well as the background. The aperture settings control how much or how little of a DOF you capture. An aperture value of 2.8 will show a much more shallow DOF than one of say 22.
Hope this helps, and again, I would expect that someone else will come along with a much more detailed answer than I.