Not just not reflecting or producing light, it doesn't interact electromagnetically at all; it doesn't emit or absorb any electromagnetic radiation. I.e. it is transparent to light and all other EM radiation. The means the only way we can detect is via its gravitational interactions. We've inferred it exists because our estimates of the total "normal" matter in the universe (and particular parts of the universe) don't account for the gravitational effects we see (e.g. the structure of galaxies and galactic clusters). Essentially there should be about 6 times more mass in the (observable) universe than we have been able to detect. We don't know what dark matter is, but most of it is not matter in the regular sense of the world. A small amount could be regular matter than we just can't detect but the majority is, at least, composed of exotic particles of a type we have yet to discover (e.g. WIMPs; the most widely accepted theory). But it could be even more exotic, e.g. it may be mass trapped in other dimensions that only gravity can access, or it may be an artefact of our laws of gravity being slightly wrong, or it could be something else.
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