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This is the Gegenschein, derived from a German word meaning "counterglow," since it is always opposite or "counter" in position to the sun in the sky.
You forget the light bouncing off the Earth on to the Moon, ... you can see that when the Moon is almost new they call it "Gegenschein" in good old German, a very weak glow on the dark side of the Moon.
In the absence of bright moonlight, he tells us,  eleven Pleiades can always be counted; the Andromeda nebula appears to the naked eye conspicuously bright, and larger than the full moon; third magnitude stars have been followed to their disappearance at the true horizon; the zodiacal light spans the heavens as a complete arch, the "Gegenschein" forming a regular part of the scenery of the heavens.
The exact nature of the Gegenschein is still somewhat of a mystery, though most think that - like the Zodiacal Light - it might be some sort of tail formed by minute particles from our atmosphere that are streaming out into space away from the Earth in the opposite direction from the sun.
The Gegenschein is visible only with the unaided eye, as it is far too large and diffuse to be viewed with a telescope or even binoculars.