For users who hate being bombarded by app notifications in Facebook, this is good news -- just don't expect notifications to disappear altogether.
Instead of using universal notifications, developers can now choose from a number of methods to communicate changes or updates to users. Facebook recommends using either counters, dashboard news notices or sending users e-mail messages (assuming they have agreed to e-mail opt-ins).
Counters, for all intents and purposes, will be just like notifications as they currently exist, except they will be specific to each individual app. If your app is bookmarked in your Facebook page, a counter indicating the number of notices you have from an app.
Facebook has also created a page of best practices for developers communicating with users.