When working with Outlook 2013, not all of your emails are listed in a folder and you get this message:
There are more items in this folder on the server. Connect to the Exchange server to view them.
After a short while you should get a link to click on saying:
Click here to view them on Microsoft Exchange
This is intentional behaviour in order to improve the performance of Outlook (and keep your user profile size down) by only synchronizing more recent emails. You can change this behaviour by clicking File -> Account Settings-> Account Settings, selecting your email account and clicking Change. From here you can move the slider bar to keep older mail.