Many spiral galaxies have flat rotation curves . If the visible mass was all there was you would expect a fall-off of velocity with distance from the core. That is what is not observed so there is evidence for some unseen matter that is "dark".

Broadly speaking two types of dark matter have been proposed. One type of dark matter is baryonic which is composed of normal matter (protons, neutrons, electrons). A second type of dark matter proposed is called non-baryonic because it is composed of exotic particles that have yet to be detected but may exist based upon particle physics. The "Cold Dark Matter" models you often hear about are referring to the non-baryonic forms of dark matter.

Tobin Dax noted that WMAP and Big Bang parameters in general seem to restrict most dark matter to the non-baryonic forms. But is important to stress that this conclusion is based upon a combination of observations and Big Bang requirements. The universe is not obligated to conform to those requirements. Some researchers have pointed to observations that suggest the dark matter may actually be entirely baryonic in nature - which conflicts with the currently preferred version of the Big Bang (concordance model --> dark energy = 73%, non-baryonic dark matter =23%, baryonic matter = 4%). So the actual census of baryonic dark matter is an important test for the concordance model.

One interesting recent result is that many elliptical galaxies have a dearth of dark matter. Other problems include observations that indicate a coupling between dark matter halos and luminous matter unexpected in CDM models.

That's why it is important to keep in mind that what the observations indicate about dark matter are more important than what any one theory says the dark matter must be.