The local storage will only be used to cache data, so that users can work offline. When they are connected, Chrome OS will synchronise local data with cloud storage.
Google will try to provide an operating environment analogous to Windows and other desktop OSs for web applications. This means web applications will be able to access graphics accelerators, mutli-core architectures and multimedia peripherals like cameras, speakers and microphones - just like normal desktop software. In fact, the whole operating system is optimised for cloud computing.
The neat thing about Google's appraoch is that any web application will run, even something like Office Live, created by Microsoft.