Private Label DNS are Private Nameservers which are configured for your domain. These can be listed on the domain record of Your customers Domains when they are hosted by your hosting service.
Example:

NameServers: ns1.yourdomain.ext
IP: XXX.XXX.XXX.XXX

NameServers: ns2.yourdomain.ext
IP: XXX.XXX.XXX.XXX

OR
NameServers: ns1.yourcompany.com
IP: XXX.XXX.XXX.XXX
NameServers: ns2.yourcompany.com
IP: XXX.XXX.XXX.XXX

With private label Nameservers, you can assign YOUR Nameservers to YOUR OWN Domain, or the Domain of Your Hosting Clients when registering new domains with Hosting, or when changing DNS records for Hosting accounts you setup for your own clients.
You can host your company site or your client sites using your own personalised name servers ns1.yourdomain.com and ns2.yourdomain.com. You can host any number of sites using the name servers with out any additional cost
The advantage of your own private label name server is when some one take whois of domain hosted with your private label name servers will see your company 'yourcompany.com' instead of our annonymous name servers hosthat.com