There are three core modules provided by Gears: a LocalServer for storing and accessing application pages offline, a Database for storing and accessing application data on the user's computer, and a WorkerPool for performing long-running tasks (such as the code that synchronizes data between your server and users' computers). For more information, follow the links.
A Gears Tutorial is available that illustrates the basic concepts. You may also find the Google Gears sample applications useful. Source code for these samples can be downloaded in a zip file found on the same page.