If you have an existing domain name, you will also need to point the domain to your new HostGator web hosting account. You can either change your name servers at your existing registrar, or transfer the domain to HostGator.
If you are not sure which to chose, you may want to read:
Change Name Servers for your Domain Name
If you want to keep your domain registered with its current registrar, then you would change the name servers to point to HostGator. The following article gives details on how to do that.
Transfer Your Domain Name Registration to HostGator
You can also transfer your domain registration to HostGator so you can manage your website and domain name with one company. The following articles will assist you with that.