I should be able to answer this one for you as I tune the systems for my job ;)
ESP (Electronic Stability Programme) or DSC or any of it's other acronyms is a 'Stability Control System' that incorporates the functions of Traction Control and ABS, EBS (Electronic Brake force Distribution) and Corner Brake Control to help the driver maintain control during an emergency manoeuvre or when there's a sudden change in grip level or when the ABS controller senses the car has lost stability (entering a skid)
Things it can do are:
-Prevent massive wheel spin during acceleration
-Prevent the wheels locking under braking
-Kill under and oversteer before it develops in to something more serious
-React quicker than any driver in an emergency situation (e.g. a high speed lane change to avoid someone pulling out in front of you).
Things it can't do are:
-Stop you crashing
-Brake to an appropriate speed for a corner.
-Pre-empt what's going to happen next. It needs a degree of wheel slip or a level of lateral acceleration/steering angle before it can react. It effectively 'catches' the car.
Providing you've slowed down for the corner in the first place, it should be virtually impossible to spin or understeer off the road. If you feel happy doing so, find yourself a deserted wet roundabout and build your speed up gradually. When the front wheels start to slip wide, the ESP will apply the inside rear brake to pull the nose back in. If you repeat this and then lift off, the car will start to oversteer, however, the ESP will brake the outside front wheel to stabilise the car. You'll hear a coarse noise a bit like a rake being dragged through gravel (honestly the best way I can describe it) which is the ABS pump running and generating pressure to apply individual brakes. The ESP light will then flash 3 times or more depending on the length of the intervention.
These days ESP systems are incredibly complicated and take a great deal of time to calibrate. Just to give you an idea.....the current Bosch ESP controller has around 20-30,000 parameters that can/must be tuned for each car!