To get this to work you firstly must install a package called "qtnx":

    sudo apt-get install qtnx

Then when you open Ubuntu Software Center you should see a new "Test drive" button next to the application screenshot.

The applications run on a remote server so you must have a decent Internet connection and also, this is not available for all the applications in the Ubuntu Software Center, but nevertheless, this feature sounds awesome.

Here's a video I've just recorded so you can see exactly how it works: