You can allow subscription to a discussion forum or thread. This means that users can choose to subscribe. If they subscribe they will receive emails when new posts are added.

To allow subscription in an existing forum:
1. Go into the relevant Blackboard course
2. Click on Course tools in the Control Panel, then click on Discussion Board
3. Click on the link to the Discussion Board and find the relevant forum
4. Next to the forum name click on the dropdown arrow, and choose Edit
5. In section 3 “Forum settings” select either Allow members to subscribe to threads or Allow members to subscribe to forum, as appropriate, then click Submit.
6. Users will then see a subscribe button in the forum or in each thread, which they should click on if they wish to receive emails.

You will have the same option to allow subscription if setting up a new forum.