Name Servers are special addresses used by domain registrars to point domains to the correct server.
In Plain English
When you buy a domain name the web needs to know where your name leads to when someone types in www.yoursite.com
Often when you buy a domain the name servers will be set to point your domain name to a page put up by the company that sold you the name. So obviously you need to change that and have the domain point to whichever company is hosting your website.
They normally look something like this
The above are the name servers for our current clouds. If you are unsure which you are on, please just pop in a support ticket giving the name of your site EG www.mysite.com and we will let you know what your name servers are.