To get to this screen, go to the Users page, and either click on the number in the Messages column for the appropriate user, or click on the appropriate user, and go to the Messages page for that user.

You can delete messages by checking the box next to them and pressing Delete
You can 'hold' messages by checking the box next to them and pressing Hold. Held messages still exist in the queue, but are invisible to email clients. This can be useful if you have a message causing a problem but you don't want to delete it.
You can move or copy messages to another user by checking the box next to them, selecting the appropriate user, and pressing Move or Copy as appropriate. Normally the message will be sent to the selected user as if it had been emailed to them, so assistants, forwarding addresses and Autoresponders etc will take effect. If you want to bypass these and send the message straight to the destination user's mailbox, check the box called Use direct copy.
To view a message, click on the text in the message subject column.