Multiplexing is in networking terms a method to process several channels of data and combined them for transmission over a single common transmission path.
There are different methods of multiplexing. Among these include:

Frequency Division Multiplexing (FDM)
Time Division Multiplexing

Multiplexing is also a term in juggling. When you throw a three ball pattern but throw more than one ball in the place of one ball, this is muliplexing. It helps to have small balls. It is a cheap and easier way to juggle 6 balls, but it is still pretty hard.

The father of multiplexing in the electronic sense was Thomas Edison. His earliest significant invention, while he was a young telegrapher, was figuring out how to send simultaneous telegraph signals over the same line therefore increasing the amount of information that could be sent over the system.

Also used in electronics to select one of multiple possible inputs. This is used in CPUs; a datapath element, such as a arithmetic logic unit (ALU), will generally need to have more than one input. For example, an ALU may take input from a register or a sign extender.

The device that handles multiplexing of this type is called a multiplexer or mux.

A sequencing approach that uses several pooled samples simultaneously, greatly increasing sequencing speed.

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From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.