What is the purpose of using the ASR system in a passenger car?

The ASR system (traction control) prevents the driving wheels from spinning (slipping) when moving off and accelerating - answer C. Preventing the wheels from locking when braking (B) is the job of ABS, and preventing skidding during engine braking (A) is the job of the MSR system.

When you press the accelerator too hard on snow, wet paving stones or gravel, a driving wheel starts to spin and loses grip. ASR detects this with wheel speed sensors, and it slightly brakes the spinning wheel or reduces engine power until the wheel regains grip. Thanks to this, the car moves off steadily and the rear does not slide sideways. The system does not increase grip - on ice you still move off gently, and when driving out of deep snow you may sometimes have to switch it off.