First time I see this. I understand jack of it but it's really amazing. On one side, it seems not too different from an abacus (it's just a machine!), on the other side there's a connection to the processor that I use right now. Very cool.
Digital electronics means thinking of a transistor as a switch. It's got three terminals, if there's a positive voltage on the control terminal then the other two are connected and power can flow through it. That's basically it.
If you connect billions of switches in the right pattern you get a computer. Billions of little switches clicking on and off, no more, no less. No pixies or magic dust involved.