At any time, the input signal is directed (switched) to exactly one of the outputs (and all other outputs are equal to 0) and the output that receves the input signal depends on the current values of the control signals.
The following figure shows schematically what a 2x4 demultiplexor does. The 2x4 decoder has 2 control signals and 4 outputs:
The following figure illustrates this many-to-many switch:
The figure on the right depicts the fact that the second input is connected to the last output.
Note that the unconnected inputs and unconnected outputs will not be active: