A singularity is basically the center point of ultimate compression in a black hole, usually said to be a collapsed star, which has burned up it's fuel supply, and ends up compressing itself, which fuses hydrogen into helium, and generates even MORE heat and gravity, until it collapses so much that it becomes a black hole. The name has often been synonymously used in place of the name: black hole, as has collapsar. The singularity itself lies beyond the "event horizon" which is the so-called point of no return for any matter/energy pulled in by the immense gravity. Spacetime inside the event horizon supposedly achieves infinite compression, and time itelf slows to a near-standstill (re: Einstein's Theory of Relativity). If you would like to get ahold of the most informed opinion and most thorough knowledge, I recommend any literature by Stephen Hawking, who is considered the foremost mind on this subject. One of his most reknowned works is: A Brief History of Time. I hope this helps.