It matters. Every site should resolve with and without the 'www' because:
- Some people will type your URL into their address bar. It's unfair to expect them to remember whether they need the 'www' or not, and not everyone will think to try the alternative if they hit an error page first.
- Others will link to your site by typing the URL and may omit the 'www', creating a broken link.
Your 'marketing people' should pick either 'www.yoursite.com' or 'yoursite.com' and redirect the other version accordingly. They might like to read the advice here to decide if they want the 'www' or not: When should I use a www subdomain?
To get the 'www' part working, they might have to add an 'A' record for the 'www' subdomain to the site's DNS records. The process differs slightly with different domain registrars, so you should tell them to contact the company they purchased the domain from to ask for help setting up the 'www' subdomain to point to the main site. (Many registrars have help pages that talk you through it.)
Redirecting the 'www' version to the non-www version (or vice-versa) differs slightly depending upon what server the website is hosted on. One of the most common servers is called Apache, and they can follow the advice listed on this post to automatically redirect visitors from one version of the domain to the other.
Finally, they should also sign up to use Google Webmaster Tools and set the preferred domain that appears in Google search results to include or omit the 'www'.