They are mail files.
And it depends... if you want any mail that's directed to that user, don't delete them. If you don't, then knock yourself out. If you're not using that username for mail at all, probably not a big deal.
Other things that may come to this user would be cron related messages, other messages from the system itself, bounces from any mail you might be sending from a CGI script, assuming you're not setting the envelope-sender properly. For all of these reasons, I think it's a good idea to check mail occasionally for your main username one way or another...
Personally, I would suggest opening them in a mail client (webmail, Pine; preferably not Outlook Express or other insecure clients if you're going to be looking at spam and viruses), and then deleting the ones you don't want.
So probably you have the DH default "catchall" alias going to your main user (on one or more domains). Disable the catchall(s). This should solve the problem. We plan on removing the default catchall soon (since we definitely don't encourage people to set one up unless it's absolutely necessary).
Probably not the problem in this case (for one thing, there would be a lot more messages).