Customize the New Post and Thread Activity notifications by going to Settings > Forum > Forum Module Settings.
New Post Admin Notification
With the Post Approval feature enabled, this email notification is sent to Admins after a new post is posted to the Forum and you determine the Admin Users that are notified by going to Settings > Portal Customization > Menu & Page Manager > click the Actions button next to Forum > Edit.
Thread Activity Notification
This email notification is sent to all subscribers of a Thread.