A popular but incorrect misconception about Office 365 is that being a Cloud Service , it is less secure as compared to On Premise Solution. The fact is that Office 365 is more secure than the regular On Premise Solution. The data which travels between the Microsoft Server and the Client device is totally encrypted.
One way in which the inherent security of Office 365 can be enhanced is by using Multi factor authentication .
For more details on the implementation of Multi Factor Authentication in Office365, please visit : http://www.techgyan.com/Pages/Multifactor_Authentication_Office365.aspx
with warm regards
Microsoft MVP 2009
Microsoft Worldwide Partner of the Year 2011 & 2007