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Black matter is also known as Dark Matter. It is essentially a hypothetical entity that explains certain oddities about the universe such as missing mass, gravitational lensing, and even the movement of galaxies. Black Matter cannot be directly detected since it does not interact with electromagnetic radiation. That is pretty hard to imagine when you consider it is electromagnetic radiation that make the portion of the universe we see visible. It can only be deduced that it exists by the gravitational effects and other hallmarks by which we also define the existence of matter.
Evidence for black matter first started to emerge in 1933 with a discovery by Swiss astrophysicist, Fritz Zwicky. He happened to be calculating the total system energy for a galaxy he was observing when the results of the calculations showed that there the galaxy had several times more mass than could actually be observed. However the theory did not start to gain validity until the introduction in the 60s and 70s of a new and more accurate way to measure the velocity of the rotations distant spiral galaxies. The findings that were found were astonishing. Even thought by most definitions of classical Newtonian physics a an irregular shaped mass should have different velocities at different points, most of the stars in the observed spiral galaxies moved at roughly the same speed. The phenomenon was also found to occur for other types of galaxies as well.
This left scientist with only two possible conclusions. One was that Newtonian physics was not as definitive as first thought and that there were scenarios in the universe that the theory did not forsee. The other was that there was actually a new type of matter that was not directly observable which would compensate for the strange movement. This is how the theory of black matter became more established.
The existence of black matter is still just theoretical and only has indirect proof at the moment. However when taking into account the mathmatices and large scale radio imaging of the known universe, many scientist believe that as much as 95% of the universe is made of dark matter. The existence of dark matter has often been cited by supporters of the Big Bang theory as evidence of the theories validity since it account for the missing mass from the explosion. However there are still scientist who are not completely sold who believe that some of the phenomenon regarding galaxies can be simply be explained as being our imperfect understanding of how gravity really works.
If you enjoyed this article there are several on Universe Today that you will be sure to enjoy. There is an interesting article on whether Dark matter powered early stars. There is also an article on Blackholes and Dark matter.
There are also some great resources online. Here is a link to a paper by Mark Hadley which best summarizes Dark Matter. You can also learn more about proof discovered concerning Dark Matter on the NASA website.
You can also check out Astronomycast. The Questions Episode for 7/23/09 talks about black matter in some depth.