If you want your server to receive e-mails, it's an SMTP server that you need.
(You'll also need to make sure that the e-mail address is set up to be sent to that server, via the MX entry in the DNS.)
Note that, depending on how you want to install this service, you might not need to write an SMTP server yourself (or even use a library). Existing SMTP servers are often capable of delegating the processing of an e-mail to external applications.
You could use somelike Postfix and configure it to use pipe for that address, to send the e-mail to process to the program of your choice (including one that you develop yourself). I'm fairly sure Exim, Sendmail and other MTAs have similar features.
With this sort of configuration, your application would usually need to be able to read the e-mail from the standard input (and have the ability to split/process headers and body), but that's usually much simpler that writing an MTA/SMTP server.
If you really want tighter integration with the MTA, perhaps this could be a good starting point (I've never tried it): http://james.apache.org/