In a nutshell. The purpose is to find out if your accumulators are actually storing enough pressure in both circuits to stop the car, especially downhill.
When the motor is running, 2 camshaft driven pushrod pumps are pumping 22-2400 psi into a regulating valve and then stored into a 2 chamber sphere (accumulator). The bottom half is pressurized with nitrogen to 1000psi. On the other side is the wetside with brake fluid.
If the motor should fail you have no brake pressure from the pumps because it has to be running. So you are going down hill, braking multiple times and you used up the stored pressure and no brakes.
The pump test simulates this condition.
Start the car and let it run 4-5 min to charge things up. Shut off and then turn key to "ON".
Press the brake pedal and let it return, repeat and count how many pedal pumps it takes to illuminate system 1 and system 2.
Let us know.
BTW it is very well detailed in the shop manuals that are online.