So the World Wide Web, often shortened to www, became a thing in 1989, and since then many people/companies/organisations have been prefixing their website URLs with www. Even though nobody ever buys www.my-website-name.com, they would purchase my-website-name.com, and the www part is a subdomain of the domain.
It is reported that the www was a mistake. It was originally meant to refer to the World Wide Web project page at CERN (Conseil européen pour la recherche nucléair) and info.cern.ch was meant to be the home page for CERN, although the DNS records were never switched. Subsequently many organisations followed suit and www became the norm.
Douglas once quipped:
The World Wide Web is the only thing I know of whose shortened form takes three times longer to say than what it’s short forDouglas Adams www pronunciation
This is because World Wide Web has 3 syllables and double-u double-u double-u has 6.
So why do people/companies/organisations use www in the URL of their site, well simply because that's how the first site did it.
What, should you do?
Well, technically, really it doesn't matter.
The way I think of it is what do you say out loud when you tell someone the URL of your site, I say - code-red.uk (that's code dash red dot uk). I, personally, would never say double-u double-u double-u dot code dash red dot uk.
How to decide?
Well if you're a company or organisation that has created loads of printed and digital materials, with either www or non-www then choose that way, the important thing to do is create the redirect on your web server.