501(c)(3) is a non-profit status that you apply for. This makes you "legitimate" as a non-profit with the IRS, allows donors to claim contributions as tax deductions, may be required if you go after grants. It's definitely got some nice benefits. However, it also formalizes you as a group. You are now on the IRS' radar and you need to be sure to file what you need to properly and on time each year.
What lots of organizations seem to do is "nothing". Technically, they aren't operating legally - as far as the IRS is concerned (if they gross more than $5000). If someone gets mad at the organization and reports you or something goes awry, the organization (and its officers) could perhaps find itself in trouble. But then again, how often to you hear about that happening? If you don't "exist" and you don't get caught, then there's nothing to file and keep up with. Believe me, I can understand the temptation to operate this way.
Whether or not you should file an IRS return isn't based on how much you carry forward or how much you "make" (like profit) each year that can then be plowed back into the school. It's based on the gross amount you bring in. So, say you have a catalog sale and the kids sell $8,000 worth of goods, you pay the company 50%, and you keep $4,000. Your gross was $8000.
If you are a 501(c)(3), then you should file a 990/990EZ if your gross receipts are more than $25,000. With less, you can file the form if you want to.
If you aren't a 501(c)(3), you are a business. The IRS doesn't know if you are donating all your profits to charity (a school) or if you a fledgling company trying to become the next Dell. You are just an entity that is earning income and must account for it. That's not to say you will necessarily PAY any taxes, but you are supposed to file.
As I stated earlier, I'm merely repeating what the IRS has told me (more than once). Each organization needs to decide for itself what to do - and if you have the resources and the need, consult a qualified tax professional.
Good luck!