Domain names are extremely important to the functionality of the internet. If you’re using the internet, you’ve used domain names. Every website is being served to you from another computer somewhere else. When connected to the internet, that computer is given a unique number to identify it. Typically, that looks like ###.###.###.### (ie, 192.168.0.256), though that is slowly changing to a new format. These numbers are called IP Addresses.
Those numbered addresses are impractical to remember, so we use Domain Names instead. The domain name for this website is clear.design. Domain names simply point to an IP Address, and make it easier to read or remember the address of a website. When you type the name of a website (google.com), you’re typing a domain name.
At the risk of oversimplifying things a bit, there are gigantic lists of domain names and their corresponding IP addresses kept by major internet providers throughout the world. When a person types a domain name into their web browser, it checks that list to see what the IP address is, and then connects to it.
Domain names are not necessary to use the internet! You can actually connect to websites directly using an IP address! But it’s much harder to keep track of which website is which if you’re only connecting to an IP address, so we mostly use Domain Names.