This is a Gnome Shell extension to show the notifications as long as you don't take any action on them. They will disappear when you click them or they hide when you hover over them.
This one is not the current version. Head over to bonzini/gnome-shell-permanent-notifications for the current version.
Easiest way to install this extension is via the Gnome Shell Extension Website.
The original extension is by @bonzini. I just made the code available here and added support for Gnome Shell 3.4.
Feel free to fork and update.