Here's the Mozilla description on WebAPI: "WebAPI is an effort by Mozilla to bridge together the gap, and have consistent APIs that will work in all web browsers, no matter the operating system. Specification drafts and implementation prototypes will be available, and it will be submitted to W3C for standardization. Security is a very important factor here, and it will be a mix of existing security measurements (e.g. asking the user for permission, like Geolocation) or coming up with new alternatives to ensure this."
The immediate items they hope to have covered by this API include dialer, address book, SMS, clock, camera, gallery, calculator, settings, games, and maps support.
To ramp up these efforts, Mozilla is also hiring developers to work on furthering WebAPI for mobile devices. This news comes just weeks after Mozilla announced their intentions to create their own web-based operating system, currently dubbed Boot To Gecko.
See the WebAPI introduction or the WebAPI Wiki for more information.