Power playing would be when someone uses a character that DOES NOT belong to them.
Now, I don't mean, say, in a public role play that someone uses InuYasha or Harry Potter...that's off of a movie or a book. They may belong to someone, but I seriously doubt that Rumiko Takahashi or J.K. Rowling role play the characters they made for books and so on.

I mean private role plays -- or even some public ones, with made-up/custom characters or people using their virtual pets and such -- as in someone suddenly controlling a character that another person is using.

Now, if this has confused you, please read the examples below.

Major Incorrection
Player 1: A large, nearly eight hundred pound feline slowly emerges from the bushes of a dense forest, his tiger-like appearance extremely intimidating, despite his temperament being very calm and mild. He sits down on a large boulder, running his rough pink tongue over his blue-striped shoulder in a grooming manner, and then lying down and placing his massive head on his large, pale blue forepaws. He flicked the tip of his long, sleek feline tail a bit, then slowly closed his emerald-green eyes while resting.

Player 2: The feline gets bored of resting and gets up, then walks away to the nearest stream and bends down to take a drink. While he does, a little blue dolphin-like creature sticks its head out of the water right where he was going to drink from! It says "Hello!" and splashes him!

Player 1: OOC: Uh, no, it does NOT, since he never got UP. If he did, you would know because ///I/// would have said that he did, not YOU. How about you go and role play with yourself? You're very good at it. =blocks=

Now, that was the major power player by not only using the character slightly, but actually taking control of it and making it do whatever they pleased. Not all are that bad, but some are even worse.
Anyway, you can probably imagine the worse ones; but for now, I'll show you the less intense ones...

Minor Incorrection
Player 1: A large, nearly eight hundred pound feline slowly emerges from the bushes of a dense forest, his tiger-like appearance extremely intimidating, despite his temperament being very calm and mild. He sits down on a large boulder, running his rough pink tongue over his blue-striped shoulder in a grooming manner, and then lying down and placing his massive head on his large, pale blue forepaws. He flicked the tip of his long, sleek feline tail a bit, then slowly closed his emerald-green eyes while resting.

Player 2: Out of the corner of the feline's eye he could see a tiny white rabbitlike creature with a red and green-striped neck frill heading towards him. "Hello!" said the bunny as it hopped up on the rock next to him.

Player 1: OOC: Uh, no, my character did NOT see yours out of the corner of his eye. His eyes were closed, and he doesn't notice your character unless //I// say he does.

See? Player #2 can't control Player 1's character..not only is it EXTREMELY rude, but what if Player #1 didn't want that to happen? What if they had an idea of their pet pretending to be asleep, and then scaring Player #2's character after it got close enough?

Even controlling another player's character a little bit is very rude and looked down upon.
You ONLY control your own character(s), and some of the surroundings if permission from the STARTER of the role play is granted. Remember, instead of just forcing Player #1's character to do what you want them to do, you can ALWAYS just ask them!

Saying "Can you please have your character get bored and go to take a drink out of a pond or stream?" is a lot nicer than saying, "_______ gets up and goes to get a drink" and controlling them.

In a role play, that's not even possible; since you're putting yourself in your CHARACTER'S position in a role play, NOT putting yourself in EVERYONE'S position.
If you're going to do that, why not just go be a writer? Then you own all of the characters and don't have to steal them from everyone else.

Now, if you want the correct example, try this one.

Correct
Player 1: A large, nearly eight hundred pound feline slowly emerges from the bushes of a dense forest, his tiger-like appearance extremely intimidating, despite his temperament being very calm and mild. He sits down on a large boulder, running his rough pink tongue over his blue-striped shoulder in a grooming manner, and then lying down and placing his massive head on his large, pale blue forepaws. He flicked the tip of his long, sleek feline tail a bit, then slowly closed his emerald-green eyes while resting.

Player 2: A little rabbit-like creature with a large frill of dense red and green-striped fur around its neck was nibbling on a couple berries from a nearby bush when its massive pointed ears noticed the sound of an extremely large animal lying down. Cautiously turning in the direction that the sound had came from, it dropped the remains of its little snack, slowly hopping forward. Staring at the giant blue tiger-like creature in awe, it blinked its large black eyes a few times, slowly venturing up onto the boulder to examine the apparently sleeping animal.

Player 1: The giant feline's rounded ears swiveled back as it listened to the tiny bunny behind it's stocky shoulders. Blinking his eyes open, he lifted his monstrous head and turned it around to look at the tiny bunny; tilting his head to one side curiously. "Hello there." He said, rolling over onto his other side with ease to face the little fuzzy white critter. "Who are you?" He asked, coiling his tail and uncoiling it as a habit.

See? MUCH nicer! Now, that bunny can decide whether to run and hide, or to simply carry on a conversation with the gentle giant. Much better than just controlling each other and making one another mad.

I hope this section was clear enough on what Power Playing is, and didn't just confuse you moreso. XD