You can set whether users need to be registered and control the registration process.
These two controls give you various degrees of control
Public viewing, public posting
By default forums are available to be publically viewed. If you set anonymous posting to be on (see 4. Above) then anyone can also post. This is the most public version of the forum. It can lead to lots of spam being posted, and does hand control of what’s said in your forums to the internet community, with you effectively being able to only delete afterwards.
Public viewing, registered user posting
Here anyone can view the forums, but only registered users can join in and post. Registration can be automatic or manual – see 6. below
private viewing, registered user posting
Here you have a private forum. Only registered users can view and post. Here it would be very unusual to allow automatic registration, and this will be typically a manual process. To set a forum as private go into dashboard>forums and select edit for the forum you wish to be hidden. Under the forum attributes on the right hand side, set visibility to private.