The Conductor is a being living in The Chamber of Columns, which is right behind the Questioning Wall. If you meet him, he might tell you where to go, if you want to get to the Wall. He has a head and a tail.
The Conductor can read souls, and tell if a soul has an evil intention. It has not been established what is considered evil by him, but sins are, for sure.
There is a conical pin at the tip of his tail, which he uses in fights. It is known to be very sharp. Few combatants got out of a fight with the Conductor alive.
The Conductor is usually carefree, and does not really care about you or your intentions, unless he considers you ‘evil’, then he will get angry at you.