A demultiplexer, or "demux," is a piece of equipment that takes a single signal carrying multiple payloads and splits it up into several streams. They are often used in telecommunications to carry signals over long distances. A demultiplexer is the opposite of a multiplexer. A multiplexer, or "mux," takes signals from many sources and puts them into a single signal. That signal is transmitted wherever it needs to go, then disassembled at the other end by a demultiplexer.
To picture how a demultiplexer works, it can be compared to the operation of a waterwheel. It is a single device with many little buckets on it that collect the water in each one. The water is then transported and then dropped off by each separate bucket. The intake of water in multiplexing, and the release on the other side is demultiplexing. It is a way of getting many pieces of traffic from one place to another without having to have separate wires for each.
In telecommunications, a multiplexer's "buckets" are timeslots. If someone is calling from an office in New York, for example, to another office in New Jersey, the call is sent from the office to the local telephone exchange. The exchange sees that the caller is calling New Jersey, so sends him to the New Jersey multiplexer. This device is directly connected to the piece of fiber that goes to New Jersey.
The call is given a timeslot, 36 in this example, and sent on its way over fiber to New Jersey. As well as the call data — the person's voice — another piece of information is put there by the multiplexer telling the other end that, while the call is in progress, anything that comes in on timeslot 36 is for this specific call. At the other end, the demultiplexer picks up the information, sees that everything coming in on timeslot 36 is for the New Jersey office, and sends it on its way via the telephone exchange.
This process of multiplexing and demultiplexing takes place hundreds of times a second for each and every conversation that takes place over longer distances. If someone was to call across the country, her conversation, still in timeslot 36, would be inspected at every major exchange and sent on its way until it reached the city she was calling. That exchange would see the call was for someone connected to it and "break out" the call and demultiplex it. The process is so refined, and the equipment so fast, that though the call data might be inspected 20 or 30 times, the caller perceives no delay in the call.