There are currently two theories for what dark matter is. The first is the
MACHO theory. MACHO stands for Massive Compact Halo Object. This basically means there are large objects orbit on the outskirts of the
milky way. These are large objects which weren't big enough to become
stars. They are probably about the mass of
Jupiter. We know that at least some MACHO's exist by the way they
lense or bend the light from a distant star. Although we have observed lensing, it doesn't occur frequently enough to account for all the mass that needs to be in the outer
halo.
The other dark matter theory is for
WIMPS. A WIMP is a Weakly Interacting Massive Particle. In this case massive means massive on an atomic scale. These particles have a tendency to not interact with other particles. They also cannot radiate away energy. Because of this they can't lose energy easily and orbit at great distances. This would explain the extra mass needed to sustain the rotation of galaxies.
It will be a long time before we have conclusive evidence as to what dark matter is and whether or not it exists.