The Communication application allows users to send messages internally as well as receive system notifications from other applications.
Communication Inbox explained
Head to Applications > Communication
On the left of the inbox, each tab stores either messages or notifications.
Messages are those sent from other individual users or groups:

They can be archived using the icon for this, and searched for keywords:

Notifications are those sent from the system and as set in a user's preferences.

They can be changed to all 'read' or deleted using the icons for this, and there is also a keyword search here:

Compose a message from either area using the icon:

Click the three dots to access notification preferences.

The In-system messenger
When browsing the Intranet, the in-system messenger bell icon will appear in the top bar (unless removed by an administrator from appearing via the Design panel)
This allows users to visually see if a new in-system notification has been received through the red bubble and perform other actions without having to navigate to Applications > Communication:

A new message can be composed, others checked and marked as read, as well as preferences accessed.