There are 4 switches and 4 LEDs, one green, one red, one yellow and one blue. The switches are connected with visible wires one to each LED. When one switch is closed, it lights up the LED that is connected to it with the same color. A basic electrical circuit,.. It can even be shown to the "victim" who, even with good electronics skills will only see a basic circuit. But then the magic happens. When you rearrange the LEDs by swapping them in their sockets, the same color switch still turns the same color LED on even though they are no more connected...
I would advice you to see directly the video to enjoy the magic first on yourself before reading further
Now, if you want to build one go there where I posted all detailed explanations:
http://www.thingiverse.com/thing:2021161