Each message can have a private text note attached to it. Notes can be viewed and edited within the user interface, by any user. They're kept private to the database (aren't included if the message gets forwarded, for instance).
A common use of notes is to attach comments or reminders to the incoming mail.
It is also possible to use them on pending outgoing messages as an "off channel" communication mean between users, when several people have to write or acknowledge a common reply before the actual sending.
When a note is attached to a message, an entry is shown in the attachments view, with an "Internal note" type where the mime type would be for a normal mail attachment, as shown in the picture below:
Private note