It is a perpetually up to date version of any future Office version, from 2013 onward, for a subscribed fee that buys you five device seats for computers and/or laptops, and five mobile devices (outside Windows Phone, as Windows Phone has Office). The installation is all local, it doesn't run from the cloud. Only cloud access applies to syncronization and Skydrive access. Still need internet access to keep Office 365 up to date.
This would be a great route, if you can actively use all five seats for devices (such as for a family with students). It would be even better if after you unsubscribe, you get to keep your last major version of Office 365 perpetually... (don't see that happening at all).
Otherwise, if you want a perpetual, always there, non-expiring license of Office, I would get Office 2013.