The root of the word conductor gives a clue that this word means

Duct means "to lead"
conductor means
1. employee on a bus, train, or other public conveyance, who is in charge of the conveyance and its passengers
2. leader, manager, director

The latin word of the word conductor is Conducere, which means 'bring together'
That was a conductor usually defined as some one who bring a group of people together and lead them. ( for example, conductor of an orchestra)

hope this helps