Like /u/Dynamic_Physics says, it‘a a switch to choose one of multiple inputs/sources for a signal.
The common reason computers (laptops) have it is to directly connect the screen to either the graphics chip built into the processor to save power or a fast gaming graphics card for performance.
This can be done without a MUX switch by always sending the signal through the slower graphics to the screen even if the gaming GPU is producing that picture. But that can decrease performance.
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