Matter that accounts for the observed gravitational attraction of galaxies which can't be observed by light. If we look at other galaxies, we can calculate their mass by watching how fast they spin. The amount of mass they have is greater than we calculate by looking at how many stars are in the galaxy and how much visible dust is there, so there's some missing "dark" (as in, doesn't interact with light much) matter. What exactly that matter IS is still a mystery. The candidates fall into two basic camps:
MACHOs (Massive compact halo objects): things like brown dwarves, small stars that are a little too small to ignite, so they're close to invisible from far away. It's almost certain that such brown dwarves exist, but it's hard to see how there could be enough of them.
WIMPs (weakly interacting massive particles): maybe there are elementary particles out there with mass (don't actually have to be heavy compared to other particles, as long as they're not massless), which would interact with gravity according to their mass but might interact with the other fundamental forces VERY weakly, as neutrinos do (I don't think neutrinos can account for the missing mass, though). If such particles exist, detecting them directly might be close to impossible.