Domain names can be thought of like a folder structure with the parent folder on the right and each subsequent child folder to the left, each separated by a dot. We've talked about TLD (or Top Level Domain) here.
The subordinate to the TLD is called the Second Level Domain name or SLD. Generally, if you are looking to purchase a “domain name”, what you are purchasing is a SLD and TLD combo. An SLD can be nearly anything. Usual choices are your company name or website “title”. So, Noisy Little Monkey's Second Level Domain name is noisylittlemonkey - which is the name of our company, without spaces or hyphens.
What’s important for Search Engines?
It used to be that when combined with a respected TLD (.co.uk, .com), a Second Level Domain that exactly matches the products or services that you sell is hard to beat in terms of getting a great ranking on search engines. However, this is less and less the case. For example, since this site is called http://underwear.co.uk/ it should rank pretty highly for a search for “Underwear”, right? WRONG: https://www.google.co.uk/search?q=underwear This is because Google is getting better and better at figuring out how to measure the public’s trust in brands such as ASOS, M&S, Debenhams, Figleaves. So, an on topic domain name can be useful, but it’s not the money printing machine it was in 2001.
What’s important for everyone else?
Don’t forget that you’ll probably want people to email you on this too, so something memorable, something trustworthy, something that’s easy to spell with a maximum of one hyphen is a pretty good rule for choosing the Second Level Domain bit of your Domain Name.
For more info on choosing a domain name, or what the component parts all mean, check out: The Anatomy of a URL