To Enable/Disable the Product Notification System
Go to Admin->Configuration->Customer Details
Change the setting for "Customer Product Notification Status" on or off according to the inline help text.

Signing Up for Notifications
While browsing products, customers sign up for product notifications via the notifications sidebox which is visible only on actual product pages (assuming you have it enabled), OR by clicking the checkboxes shown upon checkout-success, which show the products purchased on said order. Checking the boxes and clicking the submit button will opt them in to the notifications for that product. They have to have an account on your site for this to work. They manage which products they desire notification for. They manage their own subscriptions via their My Account area.

Sending Notifications
The product-notification system is not automatic. You have to send notices to the people who have opted to be notified. It is NOT to any product-changes you might make in the admin area.

To send notifications to those who have signed up, go to Admin->Tools->Newsletter/Notification Manager
Then create a newsletter/notice, choose product-notification as the type.
When sending, it will ask you which products your notice applies to. Select, and send.