VDOT is a measure of running ability and is calculated from a race performance based on Jack Daniels Running Formula. The number reflects the V̇O2max of a runner with average Running Economy. It is possible for a runner's actual V̇O2max to vary from the VDOT measure; two runners could have the same VDOT and one runner could have a higher V̇O2max with a poorer Running Economy, the other lower V̇O2max with a better Running Economy. For most purposes, VDOT is more useful than V̇O2max as it reflects actual running performance rather than a laboratory measure.
1 Meaning of "VDOT"
Note that VDOT is not an acronym, but an abbreviation of V̇O2max which is properly pronounced "V-dot-O2max" (note the dot above the V). Remember that VDOT is not the same as V̇O2max, it just uses the first few syllables.
2 VDOT and Jack Daniels Running Formula
VDOT is at the heart of Jack Daniels Running Formula. Jack Daniels' plans are based around calculating the ideal training paces based on previous race performance. The faster you are in a race, the faster you need to train. Jack Daniels book provides tables of race performances to use to look up a VDOT number. This VDOT number is then used to look up training paces for his plans. I would recommend reading Jack Daniels Running Formula, but the calculations are easier with the VDOT Calculator.