Power Points are what you expend in order to use powers. They represent willpower, grit, or in the case of Items, an abstracted fuel or a power source. Powers that are “always on,” which includes most traits, don’t require PPs, but powers that manifest a one-time effect, including Mystic Spellcasting and Psionic Manifestation, generally do.
The Power Die listed in your class description functions the same way as a Hit Die. At every class level, you roll your Power Die and add that to your pre-existing total. Like Hit Points, when you take your first superhero level, you get your full Power Die. Unlike Hit Points, you do not modify your Power Point roll by any ability score.
Also like HPs, you naturally regenerate PPs over time. Every 6 hours (i.e., 4 times a day), you regenerate a number of power points equal to your character level. If you get a full night’s sleep (or equivalent trance, meditation, etc.), then you regain all your PPs.
You can cannibalise your own body in order to fuel your powers even after you’re out of actual Power Points. Doing so requires that you trade 1 point of Constitution for a number of PPs equal to your Character Level (1 Con = 1PP / CL). This happens in the same action that you spend the PPs. Remember that as you reduce your Constitution, you also loose HPs, your Fortitude save goes down, and you reduce all your Constitution-based stats accordingly. If you reduce your Constitution to zero, then you die, instantly.
Instead of regenerating PPs, if you go into power-point deficit, you regenerate only your Constitution score by a rate of 1 per hour. Until you regenerate your full Constitution score, you do not regenerate PPs.