Mozilla is now in the early stages of developing a set of HTML5 Application Programming Interfaces (API) for building an open, web-based application interface that works across all web browsers, and that's accessible from any HTML5 smartphone or tablet.
Over at its developer blog, Mozilla explains the purpose of 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.
Of course, for WebAPI to be successful, it will require the adoption from major companies such as Google, Apple and Microsoft.
You can keep track of this project over at the MozillaWiki.