To see something you need photon coming from it. In space you see the photon from the sun bouncing on the earth and coming directly into your eyes, but any photon that bounce on the earth and miss you eye, will just keep going into space until it bounce on something. In space there is mostly empty space, so nothing for the photon to bounce, with lead to space to be black.
This is different from earth, where light bounce of everything, walls, ground, even the atmosphere.
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