OK. When it comes to email I'm a complete noob. The Github page indicates this is an SMTP server. SMTP is for sending email, right? The examples then goes into an example of creating an inbox, which indicates receiving email. Maybe someone who knows more about this might want to explain?
SMTP is the protocol that mail servers use to send messages between each other, both sending and receiving.
POP3/IMAP are protocols that your email client will use between itself and the mail server which allow you to view messages.
edit: I should note that you're correct in that SMTP is used by the client to relay email messages to the server also.
If you run your own mail server, you can usually configure it to forward mail over SMTP to a specific port, rather than delivering it to a mailbox for a client to pick up using IMAP. If you send the mail (using SMTP) to inbox.py, you'll get callbacks as soon as the mail is received, without having to worry about mailbox management and the complexity of an IMAP client.
This library is for receiving email, new email that you get, is put in your inbox. Email that you are sending goes in your outbox before it is sent. So I think it is named correctly. :)