Can a lunar eclipse completely 'turn off' the mooon, i.e. like a New Moon? Or is it always just a 'shading' of the moon (sometimes red in color)?
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No.
Lunar eclipses are caused when the Moon is in opposition to the Sun. Normally this produces a full moon, but if the Moon is in exact opposition (considering incline of the Moon's orbital plane), all direct sunlight will be blocked from the Moon:
So if all the sunlight is blocked, how can we see the Moon? Well, the main reason is that sunlight is often dispersed in the atmosphere, and so it can reach the Moon. In addition, there's airglow, which is when sunlight hits Earth's upper atmosphere and causes multiple chemical reactions, scattering light throughout the night sky.
Thus, all this light from Earth, called earthshine, reflects off the Moon and illuminates it. In addition, Earth removes and blocks parts of the sunlight's spectrum, leaving only the longer wavelengths. This causes the Moon to appear red. Lastly, because the Earth blocks off all the direct sunlight from the Sun (only diffracted sunlight and airglow reach the Moon), we can actually see Earth's shadow on the Moon.
answered Sep 21, 2016 at 18:13
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$\begingroup$ So even at a Danjon Scale value of 0 the Moon will not be completely blacked out like the Sun is during a Solar Eclipse? $\endgroup$ Commented Sep 21, 2016 at 18:42
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1$\begingroup$ I'm surprised by your statement that airglow is a major source of the light we see from the Moon during a total lunar eclipse. I've always assumed that most or all of the reddish light is sunlight refracted through Earth's atmosphere. (An observer standing on the Moon would see every sunrise and sunset simultaneously.) And the cited Wikipedia article says that airglow is generally bluish. Do you have a source saying that airglow is significant in lunar eclipses? $\endgroup$ Commented Sep 21, 2016 at 19:45
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$\begingroup$ @JakeClawson That's right. It'll be nearly invisible, but not quite invisible. $\endgroup$ Commented Sep 21, 2016 at 20:36
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1$\begingroup$ Airglow and reflected/refracted sunlight are two different things. Airglow is specifically light emitted by the atmosphere itself; it is not reflected or refracted sunlight. Your answer says that the visibility of the Moon during a total lunar eclipse is "mostly thanks to airglow". I don't believe that's correct. I think that the visibility is almost entirely due to sunlight refracted through Earth's atmosphere, with airglow making a much smaller contribution. $\endgroup$ Commented Sep 21, 2016 at 20:42
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1$\begingroup$ @KeithThompson All right, I defer to your argument. I'll make the edit. $\endgroup$ Commented Sep 21, 2016 at 20:54