UESP
Mouth is the term used for the spokesperson of a Telvanni Mage Lord. The Telvanni Council House is the assembly for Telvanni wizard affairs in Sadrith Mora, the Mage Lords themselves are far too busy and couldn’t be bothered with mundane affairs, hence they have their Mouths present instead. A somewhat justified fear of assassination by rivals may play into this as well.
Modded
Telvanni Masters can communicate with their Mouths via telepathy.1
Quote
%PCName, don’t be alarmed. I’m communicating with you via telepathy. A skill occasionally used by conjurers to link minds. Aryon may have foregone your training as his Mouth, but your formal induction into the role and the time we’ve spent working together on my research allowed me to establish a weak whisplink with you. Just like Masters do with their Mouths on the council. It appears that you marked an adequate location and through our link I’ve been able to place a spirit anchor nearby. Come speak to me.
— Galos Mathendis (dialogue)