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I have taken two photographs on a Canon crop sensor camera: 18mm f/9 with the following exiftool output (the focus was approximately at 3.5 meters):

Focus Distance Upper            : 5.27 m

Focus Distance Lower            : 1.82 m

Depth Of Field                  : inf (1.24 m - inf)

And 50mm f/1.8 with the following exiftool output:

Focus Distance Upper            : 1.99 m

Focus Distance Lower            : 1.41 m

Depth Of Field                  : 0.08 m (1.66 - 1.74 m)

Now, I assume I know what depth of field means. It's the same thing as the one that will be given by a depth of field calculator such as http://www.dofmaster.com/dofjs.html

But what are Focus Distance Upper and Focus Distance Lower?

Why in one of the pictures (shallow DoF) is the difference between focus distances higher than the DoF, and in the other picture (deep DoF) is the difference between focus distances lower than the DoF?

The Focus Distance Upper and Focus Distance Lower tags are in the Canon-proprietary "maker notes" and aren't part of standard EXIF, so documentation is scarce. However, it appears that these (together) represent the distance at which the lens's focus is set. That is, it's somewhere between the two bounds.

Why Canon does it this way rather than providing a single value (perhaps with second uncertainty or error value) is a mystery only Canon could resolve, and they don't seem to have publicly. Here's a forum post with some investigation: Re: Distance in EXIF.

Note also that Depth of Field is an exiftool composite tag. The information there is not set directly by the camera — instead, Exiftool generates this from other data, including whatever hint it gets as to focus distance. From the docs, it looks like it uses the Upper and Lower values, but also other info, which may explain the disparity you note.

In any case these values are approximate and should be taken as hints, rather than as gospel. Their original purpose is probably to hint at subject distance to aid the camera in making TTL flash power computations. They're not meant to be scientific measurements, or even photographic scene information (like GPS location tags or something).

As @mattdm found out, the FocusDistanceLower and FocusDistanceUpper, whatever they exactly mean, together denote the approximate focus distance. ExifTool then calculates depth of field based on these.

I took a look at the ExifTool source code, and the DoF calculation desires:

Desire => {

    3 => 'FocusDistance',   # focus distance in metres (0 is infinity)

    4 => 'SubjectDistance',

    5 => 'ObjectDistance',

    6 => 'ApproximateFocusDistance ',

    7 => 'FocusDistanceLower',

    8 => 'FocusDistanceUpper',

},

And if focus distance is not defined (all of 3, 4, 5 and 6 are undefined), it is calculated as follows:

$d = ($val[7] + $val[8]) / 2;

So, ExifTool is simply using the arithmetic mean of the two focus distances. Not sure if that's correct or if it's just an educated guess.

Anyway, this probably doesn't matter as I don't trust in the accuracy of focus distance fields more than I would trust in the focus distance meter on a lens that happens to have one.