To start with your second question: no, it's not a WebKit-specific feature. But although a site called ‘html5rocks’ contains a demo of this, Notifications are still not part of HTML 5. There was a discussion about them on the WHATWG mailing list this year (read the messages with subject ‘Notification API’). They are mentioned again in a later message.
So, what do we have? A description of the Notification API in Chromium. A W3C Editor's Draft of a specification, based on Chromium's API (but independent of HTML 5).
Mozilla mentioned Notifications as part of their Prism project. E.g., beginning with Prism 0.9 Notifications are a part of Prism:
The first desktop integration features
made an appearance. These included
popup notifications and dock badging. A
special JavaScript file called
webapp.js contains Prism-specific code
for customizing a web app.
You can read on on the Prism Wiki:
Prism is available as an extension for
Firefox 3 or as a standalone
application.
And from the FAQ:
Prism is the codename for the project,
and if the functionality provided by
Prism becomes a product or is
integrated into other products (like
Firefox), then it won't necessarily
continue to be called by this
codename.