A domain name is a human-friendly computer address, sometimes called a URL. The internet uses IP addresses, which are numbers, much like a telephone number. Most people find it much easier to remember names rather than strings of numbers.
A domain name is a friendly identifier (i.e., yourname.co.za) for your complicated IP address (i.e., 126.96.36.199). Which of these would you prefer to remember?
Your domain name is unique to you and when someone types it into an Internet browser they will be taken directly to your space on the Internet where they can view your website.
Having your own domain name is also quite useful when creating an email address. Instead of having firstname.lastname@example.org you could have a more credible email address such as email@example.com. This is easy to remember and much more professional.