"an open source browser extension that enables web applications to provide offline functionality:
- Store and serve application resources locally
- Store data locally in a fully-searchable relational database
At first glance, it seems to be the implementation of what Adam Bosworth envisioned when he was talking about BEA's Alchemy and browser connectivity (search for "When connectivity isn't certain" at the middle of the page).
Another potential use case for Gears is to develop browser-based desktop applications. Their main data store will be provided by Gears database which could be synchronized from time to time to a web store. Office applications (document, spreadsheets, calendar) seem like good candidate for that approach: they'll feel faster and more responsive that way. Synchronizing them will only be done when (auto) saving the document/spreadsheet/event.