When you send a Private Message (PM) to another forum user, it will remain in your Outbox until it is opened by the recipient. It then automatically goes to "Sent messages".
If a PM remains in your Outbox, it does not mean the message has not been sent. It has, it just hasn't been opened by the recipient yet.
There are 2 advantages to this:
You can edit or delete a PM as long as it's in your Outbox.
You can tell whether or not your message has been opened by the recipient.
If you receive an e-mail telling you have you have a Private Message, then you do not find one in your Inbox, it means the sender has deleted the PM. That e-mail is sent immediately when a PM is sent, and cannot be taken back if the PM is deleted.