A domain name is the unique address used to identify a website on the internet. It's the bit people type into their browser bar, like freshinc.co.uk or google.com. Without domain names, we'd all be typing in strings of numbers (IP addresses) to find websites, which would be a nightmare.
Domain names are made up of two main parts. The name itself (like "freshinc") and the extension (like ".co.uk" or ".com"). You register a domain through a domain registrar, usually for a yearly fee, and you can renew it for as long as you like.
Once registered, the domain is connected to your web hosting through DNS (Domain Name System), which points visitors to the server where your website files live. Think of the domain as your street address and the hosting as the actual building.