HTML5 has a large number of powerful APIs that make it a candidate for cross-platform development of rich desktop-type apps. One last missing piece stands in the way: unfettered access to the local filesystem: local files, thumb drives, and network shares. Perhaps someday there will be a facility to "sign" HTML5 apps to allow them access to the local filesystem, but it is not the case today.
Qt is a stopgap measure to allow you to keep 98% of your app code in HTML5, where the other 2% is Qt C++ to access the local filesystem. This preserves cross-platform capacity and potential, including to the cloud. (In contrast, a conventional Qt app without HTML5 would not be able to be hosted on the cloud.)
Below are the slides from the presentation I gave on May 13, 2013 at the Denver HTML5 Meetup group. And below that is a YouTube with audio narration, recreating the presentation.