Put in their words:
The use cases for Gears differ somewhat between mobile and desktop devices. On mobile, Gears is perfect for creating a better user experience by allowing applications to cache data more efficiently, so you can cut down on bandwidth, and carry out processes discreetly in the background. On the desktop, Gears has ideal functionality for allowing your applications to function offline and synchronize data with the server when you get back online again. You can try this out for yourself with the various Gears samples available on Google Code.