A DEMUX or demultiplexer is a digital combinational system used to send a binary signal (bit) to one from several possible outputs. A 1-to-2^N DEMUX takes a single input and selects one of 2^N outputs depending on N control signals. DEMUXes are made using logic gates.
For example, suppose we have a bit which we want to send to one of four devices depending of the situation. We must use a 1-to-4 DEMUX, send the bit as input and connect the outputs to the four devices. And what about the "situation" which I mentioned? Well, as we have four outputs to choose from, we will need to send the DEMUX a number from 0 to 3, that is: two bits. That is what we use the control signals for: if we send 00 as control signals, for example, the input bit will be sent to output number zero.
Another digital system named MUX does just the opposite (see MUX).