This is a small utility provided as part of the Mac Toolbox. It provides a way for background applications to notify the user that something has happened.
The basic problem is that a background application can't have control of the screen (ie -- demand input from the user) unless the user brings that application to the front. The Notification Manager provides a way some message can be displayed by a background application without doing anything that violates Apple's user interface guide lines..
You have already seen this utility in use (and are likely to see a lot more). One incarnation is the Alarm Clock with the little blinking symbol in the Apple menu. Another is the print monitor -- which puts up an alert to let you know that the printer has jammed during your job.