It's known as the Doctrine of the Stabilized Front (Die Standige Front), and was known to Allied planners by 1943.

A very useful document for you, in English, can be found here:

http://usacac.army.mil/cac2/cgsc/carl/wwIIspec/number17.pdf

From the document:

The Germans consider it essential to make provision for small local infantry reserves in a fortified position. These reserves are protected by strong overhead cover and can be shifted rapidly by means of underground tunnels to the area where they are required for counterattack. As soon as the attacker has taken possession of any portion of the fortified zone, these reserves are sent into action in order to strike before the enemy can organize his gains. For the counterattack, the Germans claim the defender has the advantage of a coordinated and complete observation and communication system. In addition the defender brings his sheltered reserves into action in fresh condition, without the casualties that are suffered when they pass through artillery fire, and without the loss of time entailed in bringing reserves up from the rear.

The Germans attempt to provide against the failure of the local reserves to break up an attack by arranging for additional reserves to be brought up from the rear, either by underground tunnels or by camouflaged roads. Every effort is made to give these reserves artillery support and to acquaint them thoroughly with the terrain. Sector reserves and the units of the intermediate zone may begin the counterattack without specific orders. Units with security missions do not take part in the counterattack.

It seems counter-intuitive, but this even applied to combat involving fixed fortifications. Fortified zones were supposed to be designed to allow for movement of troops and to provide for space for counterattack from a number of pre-selected points.

History of the doctrine can be found in the document's foreword. It does not appear to have been implemented prior to 1939, as mention is made of prior systems of operations.

Part of it was due to the downsizing of the Reichswehr in the aftermath of the First World War.

[W]hen Colonel General von Seekct, Chief of the Heeresleitung, looked at his resources in 1920 it was apparent that the new and diminutive German Army was insufficient even for a traditional static defence of national boundaries. The only possible solution was that it should become highly trained, mobile and able to fight a complex running battle of surprise counter attacks, retreats, and buying time (1)

This is a trade off - it reduces your manpower needs for manning a strongly fortified static defense line, but it requires the creation of a mobile reserve which requires a well trained cadre of troops and strong industrial investment in terms of armor and mechanized units.

It is also ultimately the way to deal with modern armored spearheads - it was rare that you'd be able to build up your defenses to the point where you can guarantee that an enemy would never break through, but you could contain and either cut off or blunt a breakthrough by counterattacking its flanks which requires a reserve.

Counterattacks have long been a feature of warfare (and it was actually a big component in the First World War as well - assaults that captured enemy trenches would often be counter attacked as soon as possible to try to recapture them before they could set up a strong defense line). It's probably a little more prevalent in German doctrine because they took a lot of advantage of the mobility granted by mechanization, they had a high level of initiative in junior officers, and a larger tolerance for risk "German officers were taught that inactivity was the worst sin ... the high-risk option was more likely to be correct" (2)

Sources

1. Second World War Infantry Tactics: The European Theatre by Stephen Bull

2. Ibid

It goes back to WW1 elastic defense doctrine: http://usacac.army.mil/cac2/cgsc/carl/download/csipubs/lupfer.pdf Basically the Germans would hold the line with fewer men, relying on machine guns to delay and break up attacks, while also being far less vulnerable to artillery, relying on counter attacks to inflict damage on the disrupted enemy formations and return the line to a stable position.