As mentioned in the other solution a power gem is when 4 gems of the same colour are aligned to produce a "glowing" gem of the same colour which explodes when matched up with other gems.
No two ways about it, this solution is a massive grind. You'll easily have it before finishing endless mode (I'm level 159 in that and just got this achievement). I'm well into hundreds of hours in this game spread over a few years, to give you an idea of the time committment.
One thing to note as well is the achievement doesn't pop when you get the 10,000th power gem, but rather after you get the 10,000th gem, and then quit & save back to the main menu.