You walk up to priestess Gut and she offers you the brand. If you accept it, then she brands you. Each of your companions can do the same thing.

It's the brand that allows you to use certain items, at least in Early Access.

Like, for instance, the Gloves of Power. They might Bane the enemy you're fighting if you're branded. But if you're not branded, they may Bane the enemy *and* you, because it's like a small curse type thing if you're not branded.