A MUX or multiplexer is a digital combinational system (digital circuit component) used to select one from several binary (1 or ) signals. An 2^N-to-1 MUX takes 2^N inputs and selects one of them depending on N control signals. A MUX can be made using a few AND and OR gates.
For example, suppose we have a chip with an 8-to-1 MUX. This device allows us to select one from 8 bits, which we will call I0, I1... I7. In order to select one of the inputs, we need something which tells us which one to choose, and that must be, binarily speaking, three bits, because with three bits we can code the numbers 0 to 7. The rest is obvious: we pass a number as the MUX's control signal, for example 011 (3) and the MUX's only output will match the corresponding input bit, in this case I3.
Another digital system named DEMUX does just the opposite (see DEMUX), and is the base for decoders.