First of all check if your desktop notifications are enabled in Your Account settings.
Then check the settings of your browser and see if it allows notifications to be shown.
If you use Firefox:
Press Ctrl-I on Windows or Cmd-I on a Mac. This opens a window with a “Permissions” tab. Scroll down to the very bottom until you see “Show Notifications” and see if they’re enabled.
If you use Chrome:
Go to your Settings. Then click on Content Settings. Then scroll down until you see the Notifications section. See if they’re enabled there.