Can I be blunt here? There should be a number on your health insurance card (or you can look it up) and they should answer all these kinds of questions for you in case you have follow-up questions, etc... then you can hold them accountable.
But, what it means to bring your co-pay is that each insurance policy has it's own unique terms. When you go for a service that your health insurance covers, they only cover a certain percentage of it... or they cover everything except for a certain amount of money. The money that you have to pay, in addition to what the health insurance covers, is known as the "co-pay."
In my case, I have to pay $20/visit whether I see my doctor, a chiropractor, a physical therapist, etc. That is my co-pay. Yours could be more; it could be less. They tell you to bring it but since insurance is paying most of the visit, they'll sometimes take you even if you don't bring your co-pay and just bill you later.
I have never been refused treatment for not having my co-pay. I would be you wouldn't be, either.
Best wishes, hope everything turns out ok! ;)