Braking exercise serves to inform the driver how hard their car can decelerate.
Street driving does not ordinarily call for hard braking; as such, most novice drivers apply 30-60% of peak brake torque available in their car. Especially in ABS equipped cars, drivers on a road course should be using between 90-95% of peak brake torque. Braking exercise gives the driver the experience of braking harder than they are used to in controlled conditions.
Braking exercise is normally done on one of the longer straights on the circuit. Pick an easy to see reference point well ahead of the normal braking point for the corner following the straight. Start/finish line is often a good candidate, but anything visually distinctive would work. A good rule of thumb is to start braking approximately 1.5 times to twice as far away from the corner as normal - for example, if the normal braking point is 300 feet out then braking exercise may be done starting at 450-600 feet out.
The exercise should be performed on clear track, with no cars nearby ahead or behind, and with the steering wheel completely straight.
When you get to the braking point, in an ABS car press the brake pedal as hard as you can, all the way into the floor. You should feel the ABS engage which will manifest as the brake pedal pulsating. Stay on the brakes until you are traveling way slower than your normal turn in speed, then get off the brakes and proceed normally.
In a non-ABS car you do not want to just floor the brake pedal, as this will flat spot the front tires. Instead apply more braking effort than you ordinarily do. It may take several iterations of the braking exercise to get to "full" braking capacity; that's perfectly fine.
Once you do the braking exercise you should have a better idea of the maximum brake capability of your car. Most drivers then automatically start braking harder in corners where hard braking is called for.