When you get someone to do something for you unknowingly, often the person initiating the powerplay is asserting dominance by assigning someone else a tedious task.
Let's say you and your friends have a buzzer to let you knowwhen the bbq is coming. Say... Joseph is lazy and does not want to get the food, he slyly moves the buzzer over to Andrew. The buzzer goes off...
"Andrew go get the food it's ready."
Andrew proceeds to get the food and brings it to the table. Andrew unknowingly performed an irksome task for Joseph and is powerplayed.
To unrealistically overpower your character's opponent, usually in a fight, in a chat, forum, or other text based RPG, and overstepping the bounds of realism in that particular universe. This includes a physically weaker character A beating a strong B in a fight because A's writer said so, or an inexperienced character beating an experienced one at their own game when it simply couldn't happen realistically. Related to godmodding and metagaming in that they're all dick moves
Becky used her strongest magical defense shield to protect herself
Susan kicked a hole in Becky's shield with her light blast and punched Becky in the face, in an obnoxious powerplay, since Susan just started learning magic and Becky has been practicing for years
Power Player is a person who knows where they are, and where they want to go. Everything they do is for getting them to their destination/goal, whatever that may be. PURE determinism personified in the flesh. Translated to D&D, this would be a 'True Neutral'. Basically, in their mind, NOTHING and I mean NOTHING gets in their way. If you're not helping them, best stay out of their way, because they will move through you like butter and not care at all. We're talking terminator-level persistence. They don't care what side helps them, as long as they help towards making their vision a reality.