DNS hosting is a type of network service that provides domain name system resolution services. A DNS hosting service builds, operates and provisions domain name servers, which are used and integrated with domain name registrars, Web hosting services and Internet service providers (ISP).
DNS hosting refers to static or dynamic DNS services.
A DNS hosting service is commonly provided by a domain name registrar, which often uses a backend server to provision services to Web hosting providers and ISPs. These servers are built to provide most common DNS functionality like domain translation, domain lookup and DNS forwarding. A DNS hosting service also maintains a list of configured domain names and processes all domain lookup requests from peer servers.
That being said, DNS hosting is just like Web Hosting in that anybody can do it in a small way. As with Web hosting, it's a big industry now, and while you can host your DNS with that nephew who has a server in his basement, most "industrial strength" DNS hosting providers provide 24/7 uptime, support, redundancy, etc.