Simplex communication is permanent unidirectional communication. Some of the very first serial connections between computers were simplex connections. For example, mainframes sent data to a printer and never checked to see if the printer was available or if the document printed properly since that was a human job. Simplex links are built so that the transmitter (the one talking) sends a signal and it's up to the receiving device (the listener) to figure out what was sent and to correctly do what it was told. No traffic is possible in the other direction across the same connection.
You must use connectionless protocols with simplex circuits as no acknowledgement or return traffic is possible over a simplex circuit. Satellite communication is also simplex communication. A radio signal is transmitted and it is up to the receiver to correctly determine what message has been sent and whether it arrived intact. Since televisions don't talk back to the satellites (yet), simplex communication works great in broadcast media such as radio, television and public announcement systems.
A half duplex link can communicate in only one direction, at a time. Two way communication is possible, but not simultaneously. Walkie-talkies and CB radios sort of mimic this behavior in that you cannot hear the other person if you are talking. Half-duplex connections are more common over electrical links. Since electricity won't flow unless you have a complete loop of wire, you need two pieces of wire between the two systems to form the loop. The first wire is used to transmit, the second wire is referred to as a common ground. Thus, the flow of electricity can be reversed over the transmitting wire, thereby reversing the path of communication. Electricity cannot flow in both directions simultaneously, so the link is half-duplex.
Full duplex communication is two-way communication achieved over a physical link that has the ability to communicate in both directions simultaneously. With most electrical, fiber optic, two-way radio and satellite links, this is usually achieved with more than one physical connection. Your telephone line contains two wires, one for transmit, the other for receive. This means you and your friend can both talk and listen at the same time.
Half or Full-Duplex is required for connection-oriented protocols such as TCP. A duplex circuit can be created by using two separate physical connections running in half duplex mode or simplex mode. Two way satellite communication is achived using two simplex connections.