What is dark matter?

Dark matter is stuff that we cannot "see", that is, stuff that either
(1) emits no electromagnetic radiation or
(2) does emit e-m radiation but is too faint for us to detect (today).
Dark matter may account for 90% of the mass in the universe, since "luminous" matter only contributes 5% of the critical density. We infer that lots of dark matter exists because the "gravitatational mass", inferred from the motions of objects, is much greater than the "luminous mass", inferred from the light distribution.