Think of your domain name as a street address for your website. Without a domain name, you would have to tell customers to visit your website at an IP-based url such as 22.214.171.124/~yourwebsite instead of yourwebsite.com. The former is not very memorable or friendly to human eyes and will surely result in not that many visits to your website. While it is not mandatory that you have a website domain name, nor is it mandatory that a domain you own be attached to a website, for a successful online presence you truly will want to get your own domain name to ensure your website has the proper air of professionalism and appropriate branding.
Domain names are created to make IP addresses easy to remember. Every computer has an IP address assigned to it - much like a street address. But instead of having to memorize each IP address number, we assign domain names to these numbers so we can easily remember them. The domain name system, or DNS, takes domain names and translates them into their IP addresses so that computers can communicate with one another.