Dark matter is a type of matter existing within our universe (and most likely many others) that is almost impossible to detect and has still unknown properties; hence the name "dark". Some think that it is merely large planets or black holes we haven't found yet, while others claim there is a type of particle called a WIMP that has a small but not insignificant effect on local gravity.
Dark matter is responsible, among many things, for keeping galaxies together instead of falling apart, and large quantities of dark matter can be found in superclusters too. With dark matter's gravitational effects, stars within a galaxy all move at similar speeds, which means that spiral arms maintain their structure.