From LQWiki

maildir is a structure for directories of incoming mail messages. It solves the reliability problems that plague mbox files and mh folders. Features include no locking, separate files. reliable over NFS.

There are three different folders within each maildir folder - cur, new and temp. The new folder accepts all incoming mail to that maildir. Once the email has been seen by a MUA, or mail-reading agent, the email is moved to the cur folder. The tmp folder acts as a failsafe to try to ensure no email is lost.

For a more full description and technical overview, see the man page [1].