Safari Push Notifications allow websites to send push notifications to website users even when Safari is not running.
Apple offers extensive implementation information on Safari Push Notifications on its developer website and iMore has looked at the feature previously.OS X Mavericks introduces a powerful new way to keep users engaged with your website. You can now use the Apple Push Notifications Service to send notifications to your website users, right on their Mac desktop -- even when Safari isn't running. Safari Push Notifications work just like push notifications for apps. They display your website icon and notification text, which users can click to go right to your website.
Mavericks also adds new interactivity to push notifications, allowing users to perform tasks like replying to an iMessage, or deleting an email, right from the notification. OS X Mavericks is expected to be released later this fall.
Article Link: Apple Asks Developers to Prepare for New 'Safari Push Notification' Feature in Mavericks