You need to point the MX records for the domain to a mail server.
You don’t need to do that at all. Or rather, you do, but it might not be an external email server.
When you register the domain, you set DNS records up to point an A (address) to your website (99.9% of the time which is www.) and MX records to point to where your MX (Mail eXchange) is. This may be performed directly by manipulating DNS records, or through a friendly portal / control panel provided by the domain registrar.
The MX can be an external mail server as torsoetc says. It can also be itself – ie, the MX of your domain registrar – in which case you’d then use the registrar’s control panel to define what you do with your mail. You might have mailboxes on there (typically you’d pay extra for that) or you could set rules to forward the mail on to another account such as an existing Hotmail / Gmail / ISP provided account. Or, your website hosting package might also provide mail functionality which you may choose to use, in which case your MX and A records will probably be the same IP address.
What I do is the second option. I have my domain registered with 123-reg and a website hosted by a mate who happens to own a web server. I don’t have any additional provision for email. 123-reg gives me direct access to the DNS records so I’ve defined the A record (actually, recordS as I use www. and blog.) to point to my mate’s server and the MX record to point to 123-reg. Within 123-reg’s control panel I’ve then set up email forwarding rules to say “send all email to this Gmail account” (bar a few specific addresses which are either blocked or go to other places).
So the answer to “where is my mail” is “wherever you’ve configured it to be” I’m afraid.