In telecommunication, duplex communication means that both ends of the communication can send and receive signals at the same time. Full-duplex communication is the same thing. Half-duplex is also bidirectional communication but signals can only flow in one direction at a time. Simplex communication means that communication can only flow in one direction and never flow back the other way.
An ordinary telephone conversation is a duplex communication. Most inexpensive speakerphones in conference rooms are half-duplex communication. (If you're speaking, you can't hear anyone else interrupt. You have to pause to let others speak.)