From your Settings menu, you can find the button labeled Tribe Manager. Tapping this will open the Tribe Menu if you are already in a tribe, or will prompt you to create a tribe by opening the Name Your New Tribe window.
Once you have named or joined a Tribe, you will be able to view the Tribe Menu.
Here, you can view your Tribe Members, Tribe Log, Alliances, and Tribe Governance Settings.
As the Owner or Admin of a tribe, you can manage other members of the tribe from the Tribe Member list. You can promote or demote members under your rank, remove them from the tribe, or transfer ownership to someone else. You can find out more about Tribe Invites and Member management here.
Your Tribe Log will provide information on what has occurred within your tribe recently, IE: new tames, members joining and leaving, structures being destroyed, member deaths, etc.
Your Tribe Governance Settings will determine what actions members of the tribe can take. You can find out more about Tribe Governance here.
Alliances can be formed with other tribes on your server, which allows for communication between your alliance and your tribe, as well as the ability to build near each other while ignoring the bed radius, prevents turrets from attacking tames and players. This essentially allows your tribe and alliance tribes to work together and play nearer to each other than would be possible without allying.