The registration process can be changed so that any new accounts registered on the forum will need to be approved by one of the forum's staff members before they're permitted to become a member of the forum.
To restrict members from creating new accounts on the forum until you've approved them visit the admin area and select Settings, then select Forum Settings, then Login & Registration tab.
Scroll down to the Registration Settings heading. Change the Restrict Registration option to Yes. Your changes will be applied automatically.
You'll be notified of pending registrations at the top of the main admin area and via your profile's notifications tab unless you've chosen to opt out of profile notifications. To approve an account visit the Members page in the admin area, then select Pending Registrations. Click on the Accept button next to any members you wish to approve.
The Pending Registrations page also allows you to change the forum's account approval settings without having to navigate back to your Forum Settings.