A multiplexer, abbreviated mux, is a device that has multiple inputs and one output.
The schematic symbol for multiplexers is
The truth table for a 2-to-1 multiplexer is
Using a 1-to-2 decoder as part of the circuit, we can express this circuit easily.
4-to-1 multiplexer circuit
Multiplexers can also be expanded with the same naming conventions as demultiplexers. A 4-to-1 multiplexer circuit is
That is the formal definition of a multiplexer. Informally, there is a lot of confusion. Both demultiplexers and multiplexers have similar names, abbreviations, schematic symbols and circuits, so confusion is easy.
The term multiplexer, and the abbreviation mux, are often used to also mean a demultiplexer, or a multiplexer and a demultiplexer working together. So when you hear about a multiplexer, it may mean something quite different.