It appears on the registration page, cf https://docs.mybb.com/1.6/Referrals/ (could not find it for the current MyBB version, though). Apparently, its aim is to give praise to members who refer other people to the site. And it seems it can be turned off at ACP > Settings > Login and Registration Options > Use Referrals System.
You can also access it in your User Control Panel (UCP). You can (1) see how many people you have referred to this site who then signed up to become members and (2) use the URL to send to friends and family inspiring them to sign up.
You can also access it in your User Control Panel (UCP). You can (1) see how many people you have referred to this site who then signed up to become members and (2) use the URL to send to friends and family inspiring them to sign up.