Power
You won't be deciding the fate of countries (unless you're supervising a game of RISK), but camp counselors do have a certain kind of power. You're the voice of authority for many kids. However, you're still under the camp director—and if the director says jump, you better get bouncing.
Like in any job working with children, you're going to have to be a source of responsibility and strength. The kids will look up to you, and you'll need to be assertive and confident. You could go on a power trip here, and say things like, "I said two point four minutes for cleanup! and "You macaroni-art when we tell you to macaroni-art!" But we'd advise that you don't. Young children want a confidant and a mentor, not a harsh dictator. After all, they're here to enjoy themselves.
So exert your admittedly limited power with caution. Crack down on the rules only when it's needed to ensure kids are having fun and everyone is safe. The only time to start getting really strict is if kids are wandering off into the woods, setting themselves on fire, or ruining things for others. Remember, you're the barrier between the bully and the bullied.
Also, always do what the camp director says. Seriously, they're the ones who sign your checks.