See conductor for other meanings of conductor.
A conductor is a person who sells and checks tickets on a bus, tram or train. In the case of a train, he or she is also responsible for safely closing the doors and signalling to the driver that the train is ready for departure; the conductor is the senior officer of a railway train, not the engineer/driver, as might be assumed. It varies with the public transport system whether selling tickets is a regular procedure, or something that has to be done only occasionally, if a passenger has no ticket due to ignorance, carelessness, hurry or an attempt to have a free ride (fare-dodging). In those cases usually a higher price has to be paid. This can be presented as a fine on top of the ticket price or simply as a higher fare.
Checking tickets is sometimes done at the entrance of a station or at the entrance of a train, tram or bus, in which case people without ticket can not enter.
See also: Routemaster, a bus in the United Kingdom.