GNOME Software is the built-in software management application on GNOME 3. It is a beautiful application.
In the future, it might be all you need to install and manage applications on a GNOME 3 desktop. For now, it is a work in progress. Usable, but definitely not feature-complete.
The distribution to use if you want to see how far it’s coming along is Fedora. And the best version of Fedora to download and install is Fedora Rawhide, the developmental version. Which is exactly what I did yesterday. Downloaded and installed it in a virtual environment.
The gallery below shows all the pages of the application. Note that features being implemented on Fedora Rawhide might not necessary be shipped with Fedora 20, which will be released on December 17 (2013).
Credits and license of GNOME Software.