If something’s organized, it’s arranged in a systematic, orderly way. If you’ve got a zillion baseball cards, keeping them organized is a good idea, so you can find Hank Aaron when you need him.
If you're an organized person, you keep your desk clean, your house is neat, and you keep track what you need to accomplish and when. If you're a member of the circus workers' union, you're part of the organized labor movement. You and your fellow clowns can benefit from the fact that organized workers can bargain for higher wages as a group, and that generally works better than if you try to negotiate on your own. Even if you’re funny.