Depth of field is a concept based on the fact that your eyes will tolerate a certain amount of unsharpness before the image appears fuzzy. That is, the object in the picture doesn't have to be in perfect focus to still appear sharp. For a perfect lens, at the focus plane, the image is pefectly sharp. As you move forward or backward from the focus plane the resulting image will slowly get less sharp. The distance between the point in the front of the focus plane where the image starts to appear fuzzy to the same point on the back side of the focus plane is the depth of field.
The question is: At what point does the image become fuzzy? Well, that turns out to be a rather subjective quality. To find out the amount of fuzziness that a typical person can tolerate, we need to know how small of a detail can a person see on a typical photograph. Again, this number will depend upon the size of the image, the viewing distance and viewing conditions. Thankfully, those conditions have been standardized. Most people assume that a person is viewing an image about the size of an 8 x 10 portrait; from 25 cm away. In that situation, the smallest size detail that a person with good vision can see is about 0.2 mm. Anything on the image that is 0.2 mm or smaller will be considered sharp. If I were to change the viewing distance or image size, the numbers will change and thus the depth of field will change.
Remember that the 0.2 mm minimum size is on a printed 8 x 10 image. That image is likely an enlargement of the original negative or detector size. The 0.2 mm will be proportionally smaller on the negative or detector. That size turns out to be about 0.03 mm on a 35 mm negative. This number is termed the Circle of Confusion. Most digital cameras have detectors that are smaller than a 35 mm film frame so the circle of confusion (CoC) will be proportionally smaller as the image from the detector will need to be enlarged more to get to 8 x 10 size. Digital SLR's commonly have a CoC of 0.02 mm (APS-C detector size) and most point and shoot cameras have a CoC that is considerably smaller yet (~0.005 mm). How this number translates into real life images will be discussed in the next entry.