"Blood moon" is a popular, non-scientific name for the reddish color the moon takes on during a total lunar eclipse, when it's fully within Earth's darkest shadow (the umbra).
Why red, and not black?
You might expect a moon fully in Earth's shadow to go completely dark. It doesn't, because Earth's atmosphere bends a small amount of sunlight into that shadow, and the atmosphere scatters shorter (blue) wavelengths of light more than longer (red) wavelengths — the same effect that makes sunsets look red. That filtered, reddened light is what reaches the eclipsed moon, giving it a dim copper or rust color rather than total darkness.
Essentially, a blood moon is lit by every sunrise and sunset happening on Earth at that moment, all at once, projected onto the lunar surface.
How red it looks varies
The exact shade — anywhere from bright orange-red to a very dark, almost invisible red-brown — depends on how much dust, cloud, and particulate matter is in Earth's atmosphere at the time. Eclipses following major volcanic eruptions tend to look notably darker, since ash in the upper atmosphere blocks more of the light that would otherwise reach the moon.
When's the next one?
Blood moons only happen during total lunar eclipses, which are less frequent than partial or penumbral ones. Check the eclipse calendar for the next total lunar eclipse — not every listed lunar eclipse reaches totality, so look for one specifically marked "total."