A domain is a simple URL: www.URL.com. Domain names are not case sensitive. Usually the domains branch out into subdirectories like www.AcmeMotors.com/usedcars and www.AcmeMotors.com/newcars. Subdirectory names in this case are case sensitive.
The creation of subdomains changes the examples to www.UsedCars.AcmeMotors.com and www.NewCars.AcmeMotors.com. (Of course, the www is now optional in most browsers.) And like domain names, subdomain names are not case sensitive. One obvious advantage is now AcmeMotors does not have to purchase additional URLs for their various lines of business and can direct customers more directly to the appropriate site without the need for a menu.
It is like removing the “press 1 for new cars” from the telephone menu and giving a direct line. Of course, www.AcmeMotors.com will still a general page with a menu to send the customer to “new cars” for those “not in the know.”