Notifications provide a non-intrusive way of letting the user know about things in the system. The idea is that you can use these notifications to show things that it might be interesting to let the user know about, but that they don't need to stop what they're doing to address. For example, you'd never show posting errors with a notification because you need the system to stop and for the user to address the issue right away.
Using notifications is also a great way to provide a helping hand to users who might be new to the system. For example, you can provide a notification to the user to view a video or online help article when they visit a specific page, and then hide the notification once the user has acted upon it.
Getting the notification to be displayed is as simple as subscribing to the event at a point where it makes sense to evaluate the notification. It could be when a record is retrieved from the database, when a page opens, or when a user selects a pre-determined combination of data. Once you determine where to evaluate the notification, you then add the logic that will determine whether the notification needs to be shown, which will be unique for each notification.