A half-duplex (HDX) system gives communication in both directions, but only one direction at a time. Hardly, once a party stats receiving a signal, it must need for the transmitter to stop broadcasting, before replying. A half-duplex machine is a two-party system such as a walkie-talkie, wherein one have to need "Over" or another previously designated command to show the end of transmission, and make sure that only one party transmits at a time, because both parties receive and transmit on the same frequency.
A good analogy for a half-duplex system could be a one-lane road with traffic controllers at every end. Traffic can flow in both ways, but only one direction at a time, controlled by the traffic controllers.