I did the camp about ten years ago when I was in high school. When I went, they only offered it at San Antonio. But I imagine the general ideas are still the same.
I did a little writeup on it on a previous thread:
http://www.disboards.com/showthread.php?p=24297914
As for things to pack, keep it as light as possible. They should send you a list of what to bring as far as clothes and such. Just stick to that. Beyond that, though... Maybe bring a couple books to read, some spending cash, and a camera (preferably a waterproof one). Maybe an iPod or something with headphones for at night. They keep the campers /extremely/ busy, so there's not a whole lot of time to fool around. I do recommend sending a notebook and pens. I kept a journal while I was there, it's worth doing.
When packing clothes, keep in mind that many are likely to be absolutely filthy before the end. My sweatshirt & sweatpants that I wore during fish breakout days were never the same again. Stank of fish forever, regardless of washing--ended up throwing them away. So, for don't send any nice stuff for the 'wet' clothes. The 'dry' set stayed fairly clean, though. So, no worries about those shorts & such.
Also, bring a light jacket. It's hot, it's summer... but campers will likely be spending some time in walk-in freezers and shoveling snow in penguin exhibits. Bring the jacket.
A handy thing to have is a lanyard for sunglasses, as you cannot have loose sunglasses in any of the animal areas (this applies to the employees as well as campers). They gotta be secure.
Hmm. Okay.. I just dug up my checklist from when I went (yes, I still have all my paperwork from my trip ten years ago... it was THAT special of an experience!)
Definitely bring sunscreen. Florida sun is brutal.
Oh! And a travel alarm clock.
And no jewelry. Can't wear it in the animal areas and don't want it to get stolen anyway.
This recommended a combination lock for a locker. Sounds like a good idea.
But... this was all info from 1998. So, I'd go by whatever info they send.
In general, don't overpack and don't bring extra junk. I had very, very little time to do anything after hours. But dang, if it wasn't the best time of my life! =D