We don't know much about what it does do, only what it doesn't do. Scientists have deduced its existence by measuring the speed of the expansion of the universe and determining that the mass that we can see based on the rotation of galaxies, etc. can not account for the speed of the expansion. There should be way more mass out there than there is.
We also know that it doesn't seem to react with light otherwise it would block out the stars from other galaxies as well as the cosmic background radiation. It's difficult to tell how it reacts with ordinary matter because we can't see it, but the assumption is that, since its got such a large gravitational effect, it must not react much at all otherwise it would dominate everything visible since it's 90% of the matter in the known universe.
It's difficult to make sense of what this means, but all of the other theories that explain the rotation of galaxies and the expansion of the universe don't fit very well either.
Just a clarification: galaxy rotation curves and the observed expansion of the universe are not really related.
The empirically observed expansion of the Universe is the motivating evidence for the existence of Dark Energy. Dark Matter, which is motivated (in part) by the inconsistencies in the rotation curves of galaxies is a separate topic. Despite sharing similarities in their names and the fact that they make up the two biggest chunks of energy/mass in the Universe, Dark Energy and Dark Matter are not actually related. The word 'dark' is really just implying that we have not yet observed anything to explain these two phenomenon.
We also know that it doesn't seem to react with light otherwise it would block out the stars from other galaxies as well as the cosmic background radiation. It's difficult to tell how it reacts with ordinary matter because we can't see it, but the assumption is that, since its got such a large gravitational effect, it must not react much at all otherwise it would dominate everything visible since it's 90% of the matter in the known universe.
It's difficult to make sense of what this means, but all of the other theories that explain the rotation of galaxies and the expansion of the universe don't fit very well either.