Pioneered by Dan Bernstein's qmail mail server, the maildir storage format is simplicity itself - each email is stored in a single flat text file under a home directory. One of the biggest advantages to the maildir format is that it's very difficult to corrupt, since there aren't any locking issues with multiple mail processes. Also, even if something DOES get corrupted, only one mail can be corrupted at a time, since they are all separate files.
Maildirs also perform very well in heavily loaded servers - particularly servers with heavy write traffic.
Contrast with mbox.
See also Postfix, an alternative mail server, that offers Maildir capability.