In the Volkswagen universe, the "Wolfsburg Edition" is a slightly modified production version of a particular model of a car. Sometimes it is also called a "Wolfsburg Special Edition", but that's not completely accurate because there is nothing that special about them as there have been Wolfsburg's of almost every VW made (special implies a one-time thing).
The "Wolfsburg" obviously comes from the head Volkswagen facility being located in Wolfsburg, Germany. As one person suggested to me, think of the Wolfsburg Editions of VWs as you think of the Director's Cut of a particular movie -- the stuff that the main people in charge wanted to put in but was taken out of the main version for various reasons.
Criteria for a Wolfsburg Edition varies wildly from year to year and some years are more "potent" than others. Generally speaking, the WE will only be applicable to changes in body and trim, but not to engine (these being saved for GT/GTi/GLi models). In some years, such as 1987, the WE will simply mean something like rear seat headrests and a special shift knob; in other years is means a different body kit, better seats and even frequently a special Wolfsburg-only color.
One thing that Wolfsburgs all have in common, however, as the little round badges denoting their lineage -- these are more often than naught on the front fenders close to the front door hinges and are circular enameled; They are either set on a white or black background and feature a blocky (e.g. low res) two-parapeted castle with a stylized wolf between the towers set in a shield and the words "Wolfsburg Edition" encircling the outer edge of the badge. Some of the very newest mk.IV vehicles are also Wolfsburgs, but have a oval chrome emblem without the castle, namely the 99> Jetta Wolfsburg.
These are not to be confused with the square or rectangular found on some fenders -- these square badges feature only the castle and wolf but not the "Wolfsburg edition" verbiage and are there only in the North American models to cover the holes that, in Euro models, hold the side marker lights (generally applicable to pre-A3 VW's, however, as all newer VW's come with side markers regardless of market).
You can purchase aftermarket stick-on WE badges from many supply stores, but that's just "L4M3" and you know it.. like putting a "Type R" badge on your Tercel.
obVW*: As an example, I have a 1990 Golf GL Wolfsburg. The differences between this and the base model are few, but in my opinion they really make the car worth it; that model year gave the WE larger front bumpers, Recaro seats and a better sound system. You could get these options separately, of course, except for one: in my model year the color "Tornado Red" was only available for WE's.
In North America there have been Wolfsburg Editions of the Rabbit, Golf, Jetta, Scirroco and Fox. Strangely, I don't think there are or have been WE's of the Passat/Quantum/Dasher. There are no WE's of any pre-Golf VeeDubs, as well as no WE's of the Vans, Pickups or Corrado (because it was special already).
* - Obligatory Volkswagen: in many VW communities on the net, when adding input you must also present a reference to a Volkswagen of some sort; this is frequently the one(s) you own, but can also be as simple as a funny story or VW reference.