Chatter is a built in tool for an organization to exchange information internally or externally (with partners). Just like any social application, Chatter can email notify user/s when someone posted new topic or commented on your post.
When will email notification be triggered?
1) Using ‘Follow’ feature.
When a user follows on certain event, the user will receive email notification when there is new updates on what is being followed. For example, following someone in Salesforce (including contacts) or a particular topic.
2) Group Member
When a group is created, members added into a group will receive email notification when someone posted something to the group.
3) Hash (#) tags
Hash (#) tags are used to notify someone when they are being mentioned in a particular comment or post.
In some situation, not necessarily that we will need to follow certain event to get notified. The person who post a topic can notify everyone if a group is created with everyone added as member:
While posting, click to select to show the post to only followers or a group and people who follow you or people in the group will receive email notification.
Email Notification Settings
You can also define when to receive email notification, go to My Settings -> Chatter -> Email Notifications: