Full-duplex communication occurs when workstations can send and receive data simultaneously. To support full-duplex communication, both communicating hosts should be configured to transmit in full-duplex mode. With the use of full-duplex communication, the bandwidth can effectively be doubled. Hubs are not capable of handling full-duplex communication, and you need a dedicated switch port to allow full-duplex communication.

Half-duplex is the term used for the Ethernet communication mechanism when hosts can send or receive data, but not simultaneously.

It is important that the switch and the device connected to the switch have the same duplex and speed settings, or there will intermittent connectivity and loss of connection. To verify the duplex and speed settings on a switch, execute the show interfaces command, specifying the interface and the setting can be verified (as shown in line 8 in the output below):
Switch# show interface fastethernet 0/3 Fast Ethernet 0/3 is down, line protocol is down (not connect) Hardware is Fast Ethernet, address is 00e0.1e3e.2a02 MTU 1500 bytes, BW 10000 Kbit, DLY 100 usec, rely 1/255, tx load 1/255, rxload 1/255 Encapsulation ARPA, loopback not set, Keepalive set (10 sec) Half-duplex, 100Mb/s ARP type: ARPA, ARP Timeout 04:00:00
From the output above it can be seen that the switch interface is set for half duplex and the speed is set for 100Mb/s. This means that if the host connected to this switch port is set differently, for example set to 1 Gb/s because it has a 1 Gb NIC, the host and the switch interface will not communicate and the host will not be able to connect to the network.

Multiplex is the term used when multiple signals are combined to be transferred via one signal.
Duplex implies that there are two communication paths. However, the term does not specify the required functionality, which is full duplex.