For example, the names of many hosts end in .edu. We would say they are members of the edu domain. How are all of those computers related? What do they have in common? They are at educational organizations. Similarly, if a host's domain name ends in .com, we know it is at a commercial organization. Edu and com are generic top-level domains. You can see a full list of them here.
There are also country code top-level domains like us (United State) and cl (Chile). The coolest one is tv (Tuvalu) -- video sites (Twit.tv for example) like to register their domains there. You can see a full list of the country code top-level domains here.
Second level domain names are used to identify the hosts belonging to an organization. For example, all hosts in the domain csudh.edu are related -- they are at our university.
A fully-qualified domain name identifies a particular host. For example, www.csudh.edu, identifies a particular computer in the csudh.edu domain.
Each domain has an administrator who is responsible for assigning unique names. For example, the administrator of the edu, who works at a professional organization called Educause only gave the name csudh to one second level domain, and the administrator for the csudh.edu domain, who is on our campus, only assigned one host the name www.
Note that domain registration is not tied to physical location. For example, a host that is registered in the cl domain could be located on our campus and the Twit.tv server is not in Tuvalo.
The domain names were maintained by Jon Postel and documented here. In addition to administering domain names, Postel invented and to contributed to many Internet protocols (like the one used to send email), and was the founding editor of the Internet request for comment (RFC) system.
One way to track the growth of the Internet is to see how many hosts are registered in various top-level domains. Network Wizard's domain survey has historical data going back to 1995.