Update # 1 - Webkit team has started development on web app manifest. Latest status here.
Browser push notification for Safari was introduced in OS X maverick. The Apple Push Notifications Service is used to send concise and clickable messages to your website users, on their Mac desktop, even when the safari browser isn’t running. Safari Push Notifications work just like app push notifications. They display your website icon and notification text, which users can click to go right to your website.