YouTube tutorial: https://www.youtube.com/watch?v=Q2WMlluVXmo
Analog multiplexer allows you to pass data from few pins into one.
So if you have free thermometers and you want to read all of them by single Arduino PIN, but in a different time period, then you could use analog multiplexer.
This allows you to get data from one sensor/thermometer, pass it to Arduino, then change reading PIN and pass data again to the same Arduino port. By using this technique, you can develop one software code which will do similar task to all sensors on a single Arduino port.
This works in a same way, but in oposit direction.
Asume you have one Arduino port which generates PWM signal. You want to blink three LEDs in a different time range. First second you blink one LED, then second and then third one.