In order to receive email notifications for certain events you will need to first set up email notifications.
You sub-admin will need to enable email notifications for the subscription. Then each user who wishes to receive them will need to edit their own user profile and opt for that option.
The most straight forward way to test that you are receiving email notifications is to log out of Agile Central, then click Forgot Password and type your username. This will send you an email at your registered email address on your user profile. If you did not receive that email then you may want to find and correct that issue before proceeding. You are not required to actually change your password, it is only used as a way to confirm the emails are sent and received.
More info on setting up email notifications is at: Setup Email Notifications
How to receive an email notification every time a discussion is added or modified for an artifact ?
Once email notifications are set up, you can set up a Notification Rule.
Click the down arrow which is right to your avatar -> My Settings -> Notification Rules.
Select your Work Product Type from the drop-down, you can choose between Defect, Defect Suite, User Story, Task and Test Case. Then, under the Actions link on the right hand side, click "New Notification Rule":
In the Condition section, select the Discussions field and select "Changed" operator.
This means that every time the Discussions field will change, which a new discussion is added, or a discussion is amended then the notification rule will fire and the email will be sent.