Some of the software in question spots test conditions and makes the engine behave differently during them.
It might have safety implications (e.g. deactivating airbags so they don't fire because of implausible-on-the-road vehicle states), or even enable certain tests in the first place (perhaps by disabling traction control systems confused by vastly differing speeds per axle).
Using them in order to cheat, however, is clearly not nice at all.
Speaking as a German, and as someone who has worked in the automotive industry, I'd really like for manufacturers to be punished hard on this.
The amount of complacency and disdain for regulations on the part of the manufacturers is disappointing, and the collusion by the German government distasteful.