The way I've had it explained to me is the f stop indicates (loosely) the total number of feet in front/back of the focal point that will be in focus. Roughly translated to 1/3 in front of the focal point and 2/3 in back.

For close object, an f-stop of 2.8 would mean 1 foot in front of the subject and 2 feet in back of the subject would be in focus or Fuzzy Background.

For close objects, an f-stop of 8.0 would roughly mean lots would be in focus in front and in back of the subject. Sharp background.

f-stops are basically irrelevant in cases of shooting subjects far way.

Is that correct?