Psy Points (also called PsP) are points used to execute certain actions that depend upon great mental exertion. They behave similarly to Magic/Mana Points in other games. With the exceptions of TRPG1 and Telepath Tactics, characters all begin every battle with their maximum Psy Points. They then deplete them as they use PsP-dependent attacks. A character with Psy Points lower than the required PsP cost of an attack cannot execute that attack.
Psy Points can be regenerated by focusing (accomplished in TRPG2, TSoG and Telepath Tactics by either not moving or not attacking on any given turn). Psy Points may also be recovered via a Transfer from another character. Yellow orb can also help increase regeration considerably.
In TRPG 2, TPA1 and TPA2, the maximum amount of Psy Points for the Heroes is 99, which means that the Psy Power stat is maxed out at 50. The other characters, however, don't face this 'problem' and can have as many Psy Points as one wishes.
In Telepath RPG: SoG, Duvalier's maximum possible amount of PsP is 149.