Starting with Firefox 44, websites can send messages to users if they agree through Push mechanism, these are called Push Notifications. Until and unless you give permission, no service will send you these push messages, but a site can ask you to show notifications.

For instance, since Yahoo mail supports desktop notifications in Firefox, it requests the user like this: ‘Would you like to receive notifications from this site’ and you’ve three options: Always Receive Notifications, Always Block Notifications, and Not Now.

Yahoo mail site asking user to receive notifications in Firefox 44

If you’ve accepted to receive notifications, then follow the below steps to stop getting notifications from that site or multiple sites.

1. Click on Firefox Menu, select  > Options > Content, click on ‘Choose’ under ‘Notifications‘,

2. Select the site and click ‘remove site

Manage site notifications in Firefox

To remove all websites that are showing notifications, you need to click Remove All Sites button.

FYI, Firefox also offers ‘Do not Disturb me’ button in the Content Section of Settings for Notifications, which, when enabled, no notifications from websites will be shown to the user until the restart of Firefox browser, this is a temporary fix.

To permanently disable or turn off desktop and Push notifications in Firefox

1.Visit about:config

2. Find the preference dom.webnotifications.enabled and change its value to false.

3. Done.

From now on, no website will request you to show notifications in Firefox browser, including those related to desktop.

UPDATE: Firefox 59 offers New Settings to disable Notifications