IMAP servers provide access to existing mail, in existing mailboxes. IMAP servers are not involved in the mail delivery process. You'll still need to have your mail server software receive mail via SMTP and place it in recipients' mailboxes.
It does not matter to the Courier IMAP server which mail server you use: Sendmail, Postfix, or something else, as long as the mail gets delivered to the correct mailbox. The Courier IMAP server just reads mail from existing mail accounts, without needing to know how it gets there.
The Courier IMAP server
uses "maildirs" to store its mail. Please note that this
IMAP server does NOT use
traditional mailbox files (
/var/spool/mail, and derivatives), it was
written and optimized for the specific purpose of providing
IMAP access to Maildirs.
Consult your mail server's documentation for help on how to get
it to deliver mail in the "maildir" format.
"Maildir" is a directory-based mail storage format originally introduced in the Qmail mail server, and adopted as an alternative mail storage format by both Exim and Postfix. The Courier IMAP server is a popular combination with Qmail, Exim, and Postfix servers that are configured to use maildirs. The primary advantage of maildirs is that multiple applications can access the same Maildir simultaneously without requiring any kind of locking whatsoever. Maildir is a faster and more efficient way to store mail. It works particularly well over NFS, which has a long history of locking-related woes.
The Courier IMAP server implements several extensions to the basic Maildir mail storage format in order to support some additional features, such as folders and "soft" quotas. This is done in a way that's backwards compatible with the standard Maildir users (although, of course, they will ignore the additional features). Other software that understands and uses the same Maildir extensions is SqWebMail, and maildrop.