Domain names may not seem that important but are essential if you want to have a school Web site or use an email service for your staff or students. Without registering and hosting a domain name neither of these is possible!
A domain name is the part of the email address that comes after the '@', ie *******@rm.com or the part of the Web site address that comes between 'www' and the next forward slash ie www.rm.com/support. So RM's domain name is 'rm.com'. They're basically an easier way of remembering a complicated numerical address, ie www.rm.com is 220.127.116.11.
The difference between hosting and registration of domain names
Domain name registration gives you the exclusive right to use that domain name, whereas domain name hosting allows that domain name to actually be used.