This is the first part of the web address or URL displayed in the long thin box towards the top of your browser window.
The Domain name for this site is nigelbunner.co.uk. Think of it like a postal address — you just need to type in the domain name with http://www at the beginning of it and your browser takes you to that particular web site.
You need to buy a Domain Name for your website so that people know where to go to to look for it. Domain names usually cost around £10 for 2 years for .co.uk domains and around £30 for .com domains. Some companies include the Domain Name when you buy hosting from them.