I'll see if I can break it down into a brief but clear description (some of this you probably already know, but it might be helpful to someone to describe the whole thing)...
All computers on the internet have an IP address that is used just like a street address on your house. It's how computer A knows how to reach Computer B. But the IP addresses are hard for humans to remember.
So we have the domain name system. You register a domain name so that it becomes yours to control. So when someone wants to connect to you, they can use the names you create within your domain. However, in order to translate the human friendly names you define to computer friendly addresses, the computer has to do a lookup through the domain name system (DNS).
DNS needs a way to make sure the addresses it's translating are correct, so this is why you define certain nameservers to be authoritive. This means that only the nameservers you set in your domain are allowed to define the names and corresponding addresses for your domains, so any DNS server that doesn't have your host names cached will query your authoritive nameservers for that information.
And that's the simplistic description of the domain name system
Your DNS server information are provided to you in your welcome message when you activated your hosting account.
