image credit: John Vickery and Jim Matthes/Adam Block/NOAO/AURA/NSF; image source; larger image
This is NGC 3198, a spiral galaxy. Astronomers originally assumed that most of the mass in this kind of galaxy was concentrated in the bright central region and, therefore, that the stars in the spiral arms moved in circular gravitational orbits--like the planets in the solar system. But when astronomers measured how the stars move, they could not explain the rate of rotation based on the stars they could see in the galaxy ( Rotation Curves for results for NGC 3198). In particular, the mass of the stars was much too small to produce enough gravitational force to explain the observed rotation. They were forced to the conclusion that much of the mass in galaxies does not emit light (thus the name "dark matter").
(This feature was updated on July 31, 2013.)
Imagine a universe where physicists understand only a small percentage of the matter in it--that's the situation today with the Missing Mass, one of the great unsolved questions in physics. For a discussion of the observations that led to this challenging situation, visit the Wikipedia entry Dark Matter.