Office 365 works best with the latest version of Office, Office 2010, and Office 2011 for Mac. Office 365 works with Office 2007 with slightly limited functionality.
If you have an earlier edition of Office, you will need to update to a newer version of Office in order to use Office 365; or you can subscribe to one of the many Office 365 plans that include the latest version of the Office suite.
In addition to getting the latest version of Office as part of your subscription, you will also get automatic updates, so you will always be up to date.