How to view the notification area in GNOME?

This is known as Message tray in GNOME 3. It contains all the notifications that you have not acted upon or that permanently reside in it. It also shows the status icons of your running programs (which uses it).

The message tray is hidden by default. It appears when you move your mouse to the bottom screen edge and let the mouse rest there for a short period of time, or press Super + M. You can close the message tray by pressing Super + M again or Esc.

The new message tray was added in GNOME 3.6 with lots of improvements over the old one. See the release notes of GNOME 3.6 for more information.