You must enable notifications. In order to do so, from the “My Snap” page, tap on the video feed to open up the Snap in question. Tap on the gear icon to open up Settings; in it there is an option to enable the notifications.
Check your mobile device’s notification settings to ensure that Snap’s notifications are enabled.
On iOS, go to your Settings and then tap on Notifications. Make sure Snap has “Allow Notifications” enabled.
On Android, go to your System Settings and then tap on Notifications. Make sure Snap is set to “Normal”.