When a member of a group, users can be notified about certain actions and engagements from other members
As a member of a group, users can adjust their notifications on a per-group basis. by clicking on the SETTINGS of the group, they can adjust their interaction for that group: 
Follow: Would you like content from this group in your home feed?
Post Notifications: Would you like to be notified about new posts in this group?
Display On Profile: Would you like this group to appear visible on your profile?
NOTE: Adjustments made to a group are only tied to THAT group - they do not apply to ALL groups unless the user adjusts their notifications at the account level.
There is also the configuration at the PROFILE level where a user can control the chat activity notifications for all of the groups (combined) and toggle what notifications they would like to adjust:
Chat Activity: A user will receive chat activity notification when there are new chats made in the group
[Verified] Joined The Chat: If a verified member of the community joins the chat, then this will also act as a notification sent! If you're not using verified, this toggle will not appear. The other point is that you see "Honeycommb" here, which will change based on your translation of verified
You Were Mentioned: If a user is mentioned in a group chat, it will send a push notification