In short, the answer is that there is no atmosphere in space! Before getting into why not having an atmosphere is a factor, let's see what is the importance of having an atmosphere in terms of being able to see light.
So, the atmosphere basically scatters light so it's visible to us! Now, what is the scattering of light? Scattering of light as defined by many is that when sunlight enters the atmosphere of the earth, the atoms and molecules of different gasses present in the air absorb the light and then re-emit light in all directions. Now, we know that we can see light only if it's scattered, and it can only be scattered if a layer of atmosphere is present.
Coming back to our question about why is space dark, as we know there is no atmosphere in space so the light is not scattered, and therefore we assume that space is dark. Fun fact! Space isn't completely dark! If you look at the sun there will be a lot of white light coming from it but if you look away from the sun you will see complete darks except for the few stars in the middle.
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