Growl is the non-Apple third party app that is the de-facto standard for notification on Mac OS X. Growl sits on top of your menu bar quietly upon launch, and will alert you of happening in Mac OS X by third party apps that supports Growl.
There are many third party apps supporting Growl. The list includes major apps such as Firefox, Twitter and Skype among others. Growl will remain the standard mean of notification on Mac OS X until there is one coming directly from Apple. We suspect Apple will soon release a notification system on Mac OS X similar to what is available under iOS.