1520s, "one who leads or guides," from French conductour (14c., Old French conduitor), from Latin conductor "one who hires, contractor," in Late Latin "a carrier," from conductus, past participle of conducere "to lead or bring together, contribute, serve," from assimilated form of com "with, together" (see con-) + ducere "to lead" (from PIE root *deuk- "to lead").
Earlier in same sense was conduitour (early 15c., from Old French conduitor). Meaning "a director or manager" is from 1630s; specific sense of "leader of an orchestra or chorus" is from 1784. Meaning "one who has charge of passengers and collects fares on a railroad" is 1832, American English. Physics sense of "object or device that passes heat or other energy" is from 1745; of electricity from 1737.
The office of conductor in the modern sense was not clearly distinguished from that of leader until about 1800; formerly the leader played an instrument, usually the harpsichord [Century Dictionary]