According to the support document:
If you don't have an option for Notifications in the Settings menu, then you don't have an app installed that supports notifications.
An app needs to be used at least once before it will receive any notifications.
The iPod Touch can receive notifications any time when the screen is on and Wi-Fi is connected. If the screen is asleep, the iPod Touch will check every 15 minutes for a notification.
You can disable notifications for an app in the Settings menu
If you restore a backup to your iPhone or iPod Touch, you'll need to use an app at least once to get notifications again.