Multiplexing basically involves taking multiple signals and combining them into one signal for transmission over a single medium, such as a telephone line. The input signals can be either analog or digital. The purpose of multiplexing is to enable signals to be transmitted more efficiently over a given communication channel, thereby decreasing transmission costs.
A device called a multiplexer (often shortened to "mux") combines the input signals into one signal. When the multiplexed signal needs to be separated into its component signals (for example, when your email is to be delivered to its destination), a device called a demultiplexer (or "demux") is used.