In order to see light, something must be producing the glow, but the space between galaxies is largely empty so we observe this space to be black. Despite the fact that there is some material between galaxies, strung in a cosmic web, the density of this material is very low and any light that is emitted or reflected would be incredibly faint in comparison to that which we can see from galaxies.
Couple this with the fact that the space between galaxies is also, theoretically, populated with incredibly dense dark matter, which as its name suggests does not emit light, and you are left with what appears to be an empty void.
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