By default, tribes are open to anyone who would like to follow it.
Some tribes may not want to let anyone jump in the tribe as a follower. For those tribes the Chief can choose to "protect" the tribe. This means that the only way for someone to come into the tribe is through an invite from the Chief.
To protect a tribe, go to the tribe page and click the "settings" button to the right of the "conversations" tab.
Inside the "settings" overlay, check the "Protect my Tribe" checkbox.