The notification bar refers to the messages that appear in a banner on the top of the page until you dismiss them. These banners are used to welcome new users, inform users of new privileges they've gained among other messages.

For questions relating to the notification bar. The notification bar refers to the messages that appear in a banner on the top of the page until you dismiss them. These banners are used to welcome new users, inform users of new privileges they've gained among other messages.

Stack Overflow welcome notification bar

In the image above, the notification bar is the orange bar welcoming new users to Stack Overflow. The X in the corner is used to dismiss the message.