basically, it works like this: you go to your wallet and once you earn some Hive, you Power up. This converts Hive into Hive Power, and now your account can run on its own without someone else delegating you Hive Power.
If you want to cash out, you Power Down which converts Hive Power back into Hive that you can sell on an exchange. But having Hive Power causes two things: your likes (upvotes) turn into money for authors, and you earn rewards on curating posts too.