there is a lot of verbal fog around this, so beware of reading to much about it

Usually "power-shifting" means up shifting without engaging - or at least without fully engaging - the clutch.
You may have observed gears can be changed without engaging the clutch if done with some ease and play with the throttle - if you happened to experience a clutch failure

With up-shifting in higher revs it is sufficient to just ease throttle down a bit for a tiny moment to let the higher gear "slip in" (needs some practice and an "light foot"

), no clutch needed. If it's done smoothly damage to the transmission is minimal to none. But
1. never even think of doing so with down-shifting!
2. do the practicing with someone else's bike

In the end this gives you just some little advance over "conventional" shifting as he transmission is never fully disengaged. Very valuable especially when up-shifting while cornering.
But there are many different views about this topic ...