I'm very excited and impressed by reading through the developer documentation and demonstrations. The architecture employs a switch based on a installed browser plugin and decide whether to retrieve the data from server or from a local database installed on the client.
I played around with the demo's a bit and it seems that the browser database seems to be specific to the browser. For instance if you browse a particular site using Firefox and create local copy and then open IE for offline browsing it wont be available offline. I'm curious to research more and see if developers can actually take advantage of the API and bring offline sync support to multiple browsers. Overall I am impressed and excited about the technology.
Also there is a offline version of Google Reader released recently.
UPDATE: Google Developer Day -- Google Gears Intro Video