A domain name in its simplest form is just an Internet Website address. Just as your house or apartment has its own unique identifying address for the post office, so does each and every Website in existence.
The domain name system was originally created for the benefit of humans. The actual address used by computers is numerical in format and is referred to as an IP, or Internet Protocol, address. An IP address takes the form of four series of numbers separated by periods. An example of an IP address is 215.55.258.145, and as you can see this would not be easy for most of us to remember. So to compensate, the domain "name" system was created. Its much easier to remember a website named "thiswebsite.com" than it is to remember a number such as the one above, right?