I think Scott Guthrie first mentioned the ability to take Silverlight applications offline in his keynote on Tuesday. It raised a few eyebrows but few details were forthcoming on how exactly this was accomplished. The answer is that you can create Silverlight applications that run inside Live Mesh (specifically they run on the Live Operating Environment) and can run both on and offline. Mesh applications are themselves mesh objects and are sync'd across your mesh of devices so can be accessed from any of your Mesh devices or the Live Desktop. They can also access other mesh datafeeds and objects so, for example, with appropriate user consent they can access the user's contacts, Live folders etc.
The diagram on the right is a Live Framework architecture overview which should provide some context. To understand more I'd suggest watching the following PDC sessions:
- BB30 Live Services: Building Mesh-Enabled Web Applications Using the Live Framework
- BB31 Live Services: FeedSync and Mesh Synchronization Services
Neither of the session recordings are available at the time of writing but you'll be able to find them at https://sessions.microsoftpdc.com/public/timeline.aspx shortly.