When it detects one or more driven wheels spinning significantly faster than another, it invokes the ABS electronic control unit to apply brake friction to wheels spinning with lessened traction. Braking action on slipping wheel(s) will cause power transfer to the wheel axle(s) with traction due to the mechanical action within the differential.
All-wheel drive (AWD) vehicles often have an electronically controlled coupling system in the transfer case or transaxle engaged (active part-time AWD), or locked-up tighter (in a true full-time set up driving all wheels with some power all the time) to supply non-slipping wheels with torque.
This takes place with the powertrain computer reducing the available engine torque by electronically limiting throttle application and/or fuel delivery, retarding ignition spark, completely shutting down engine cylinders, and a number of other methods, depending on the vehicle and how much technology is used to control the engine and transmission. There are times when traction control is not needed, such as trying to get a vehicle unstuck in snow or mud.
It only allows one wheel to spin which would propel a vehicle enough to get it unstuck, whereas both wheels applying a limited amount of power will not produce the same effect. Many vehicles have a traction control shut-down switch for such instances.