As a web developer who has just begun building native apps: running outside of the various sandboxes browser based apps are quarantined in. Deeper file system access, better access to hardware and sensors, notifications where helpful, deeper integration into the operating system (open with, file previews, widgets to launch the app, etc) and performance. Some things the web does well, some things it does less well than native. With a native wrapper around a web app you can leverage the best of both!