In the last time I worked a lot on my Exchange 2013, SQL 2012 and Sharepoint 2012 lab. A really nice feature is the Exchange 2013 Offline OWA.
You can start using OWA offline from the OWA Website:
OWA informs you to that it will save some content of your mailbox on the computer.
What you can see now is that OWA safes mailbox content on your local disk under C:\Users\user\AppData\Local\Microsoft\Internet Explorer\Indexed DB
Like Exchange also the offline files are some edb an log files.
There is a full list of all offline OWA features: http://technet.microsoft.com/en-us/library/aa997437(v=exchg.80).aspx