Public vs. Private Forums
When you set up a discussion topic, you are prompted to set it as "Publicly Available" or "Members Only".
As long as the Forums page has not been set to "Secure" in Menu / Page Maintenance, it will display all topics and messages for all forums items marked as public. Any visitor to your site can read the messages, though they do not see the author's information.
When a member logs in, that person will see boh the public and private discussion topics and messages. Also, they will be able to see who the author of each message is.
No person who is not logged in can write messages to any discussion topic. If they could, you would need to constantly monitor your forums to make sure that messages of an undesirable nature did not come to being.