What are companies and individuals looking for when they check your credit?

I am at a total loss to figure out how FICO scores work. My score was at a certain level (a pretty good level actually) about 4 months ago. Since then I paid off and closed about 5 accounts, and paid down 2 others, and my score goes DOWN? Is it lots of accounts with no balance but open, or few accounts open but low balance, is there even any medium you can follow to maximize your credit score? How does it work, it's like trying to understand car insurance rates!