Power fantasy is being so strong that you thwart your opponents' plays just by existing - to be so far and unbreakable as to render attempts to damage you futile. You know in "Meet the Medic" when Heavy shouts "I'm Bulletproooooof"? That's what we want to feel when we dive head first into the enemy team, laughing at their pitiful efforts to even effect us. Leona's "Next time, try to leave a scratch" is another good quote
More realistically, tanks are generally the class that's first in a fight, last out of it. When they're strong, they can pick fights with little fear of retribution. You can walk up to a fed assassin and glue yourself to his ass, repeatedly telling him to go fuck himself as he desperately burns everything trying to get past your thick, unbudgeable body. You can bathe under towers and shower in MF's ult.
When tanks are strong, they dictate the rules of engagement: "Ok, we're fighting here, and we're fighting now. No, I don't want to fight anymore. I'm going home". They get to punish over aggression or overly passive play - the Riven or Yasuo or Pantheon that's so desperate to get kills and snowball, that would be a huge pain in the ass for anyone else? You get to laugh as they rage when their faceroll doesn't feed then kills, tilt, and try to dive you - only to die, thrashing pathetically against your durability. Meanwhile, the Ezreal or Nidalee or Ziggs that hides a million miles away and takes pot shots? You laugh at them. You casually stroll between them and your damage, soaking up all the skillshots as your adc takes tower. You wade under their tower and shove their face in the ground, laughing as they use their escape only to fall to your diver or assassin.