When search engines started indexing the world wide web, they worked by following links from one website to another, and if the first website had an embedded link that included the prefix, then all pages of the website would get indexed with the www. prefix included. However, if the first website had an embedded link that did not use the www. prefix, then all of the pages of the website would get indexed without the www.prefix included.
All search engines nowadays should recognise this issue and treat the two versions of the website as being the same, however which version is used in search results may depend on which version of the domain name is used most on other websites, and the way they are ranked in search results my also differ.
Google provides a mechanism described at https://support.google.com/webmasters/answer/44231?hl=en whereby you can tell it which of the domain names you would prefer to be treated as the 'canonical' version. Once the preference is set, Google will always translate non-canonical domain names into the canonical versions before indexing each page of the website, and search results will always use the canonical domain name.
However, some search engines may be incapable of spotting that the www. and non-www versions of a domain represent the same website, or may not offer the ability to choose which you prefer to have treated as the canonical domain. In these cases it may be preferable to configure the web server that hosts the website to respond to any attempt to view a page using the non-www version of the domain name, by directing the user automatically (using what is called a 301 redirect) to the same page on www version of the domain. The reverse is also possible where people attempting to view the www version will be redirected to the non-www version.
The method by which these redirects to and from the www and non-www of the domain names varies depending on which web server is used to host the web site.
At present the majority of pre-existing websites hosted by it'seeze are accessible via both the www and non-www versions of the domain name, but if any customer prefers for us (usually at the advice of an SEO company) to reconfigure the website to use redirects between the different versions, then we will set this up for them. The customer just needs to tell us whether they would prefer the website to be accessed via the www or non-www version of the domain name.
Going forward, all new websites are being made live with the www version of the domain name being the 'canonical' version, and all attempts to access the non-www version will be redirected to the www version. Of course, if any customer would prefer their website to be accessed using the non-www version of the domain name, we can configure the web server to reverse the redirection for their website.