The notification icon, subsequently called badge icon, is an indicator of new events right next/on top of the app icon.
The automatic display of the badge icon for new events can take up to an hour, as the system always has to check for new events every hour for each user.
There may be various reasons why no badge icon is displayed on your device:
On iOS, the badge icon disappears as soon as the app is opened (it only reappears when new messages are received).
The settings may differ depending on the device or operating system version, but the settings path for activating/deactivating should basically look something like this:
Settings -> Notifications -> Enable/Disable Icon Badge
Attention: Older devices or operating system versions do NOT support badge icons. Please verify if your device supports badge icons.
Examples of cases where badges should appear on the app icon:
Examples of cases where NO badges should appear on the app icon: