To view private messages between registered users on your site, click on the Private messages model within then Accounts application.

Select the private message you wish to troubleshoot further.

From this view, you can see the user's username and user id, as well as the recipients.  You are able to see the message they sent as well as the date and time it was sent. This information is displayed for troubleshooting purposes so you can further track down these users and the date/time's in logs or other area's of the admin to determine the cause of the user's issues.  

You can then Save, Delete, or continue editing the item.