What is the origin of the power button? Is it supposed to resemble a physical switch?
Was it originally skeuomorphic UI design? Did it every move/turn or provide feedback?
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It's a stylised form of the '1' and the '0' for 'On' and 'Off'. You can see the evolution here.
This symbol is comprised of a 1, indicating "on", and a 0, indicating "off".
It was originally designed to indicate "standby", or a low power state that was neither truly on or off. At that time, a 1 inside of a 0 was the power symbol.
On December 8, 2004, IEEE 1621 designated the former standby symbol as the new power symbol and designated a waning moon as the official "standby", or "sleep", symbol.
While only conjecture and not supported by any evidence, this article makes a pretty good case for the evolution of the standby button: http://designblog.nzeldes.com/2008/05/the-evolution-of-the-onoff-power-switch-symbol/
The short version is that as rocker or toggle switches were replaced by momentary push-button switches the I / O symbols were merged to fit the single button interface.
I must say the other answers are pretty convincing and they have a substantial basis in the references cited, but I believe there is another intepretation worth considering. Yet be advised: this is pure conjecture.
When you come to think about the word circuit, you will realize it resembles the word circle, and not only in English. A mechanical power button is, more or less, just a way of closing/opening the circuit. Power supply, capacitors are usually marked with perpendicular lines if I am not mistaken. I always posited that the button simply represents connecting/disconnecting of the circuit.
I write it only as an interesting (I hope) minority report, however, as I cannot provide any evidence that this is how it actually came to be.
The statement I heard within IBM at the time was that this was a visual pun of sorts. Yes, the overlaid 1/0 idea was there, but the primary reference (it was claimed) was to the engineering schematic symbol for a particular kind of valve -- one in which the valve shaft rotates a disk to either block or permit flow through the pipe -- and thus was more directly intended to convey power on/off.
Take this with appropriate dose of skepticism, but i believe I have seen that use of this symbol.
The goal, of course, was to internationalize the machine, back in the days when human factor experts were rediscovering the idea of icons...and others were pointing out that icons weren't universal either, as demonstrated by the general dominance of alphabets over hieroglyphs. Whatever they did was going to generate complaints.