"dumb down" is just self deprecating :-(. I've always had "brains" and been an "intellectual" but i thought anarchists were pretty worthless human beings for most of my involvement in politics.
As dot says, it's a total absence of institutional power, power that's maintained by a post or a static (unchanging) group...it seems pretty true that there will always be imbalances of "power" (humans can be competitive and and fight over resources, it's a way they can choose to be). For example, differences in the way members of a group treat each other wil always occur cuz luckily were not all the same, but having a position like kingship keeps massive hardships in place and offers little chance for changing conditions. Just like how in the USA people struggle financially and see no end to it while banks suck the money out of them with incomprehensible processes. People claim you can "move up if you try hard enough" but our society encourages fast-paced competition, and the wealthy spending a lot of money maintaining the illusion of a fair and just system. If we're all supposed to respect authority and keep moving forward, how can we think for ourselves?
To me anarchy means striving towards a world not so hampered down by laws, the state isn't all that powerful but it's logic is contagious and it relies on fear or else it would all come tumbling down like a house of cards.