A gravitational singularity (sometimes called a spacetime singularity) is a term used to describe the center of a black hole where gravity is thought to approach infinity. Some physicists, however, do not think that spacetime actually goes to infinity, even thought the singularity is approached.
In the center of each black hole is a singularity, a point where infinite density develops as spacetime approaches it. Spacetime goes toward infinite curvature and matter is crushed to infinite density under the pull of infinite gravity. At a singularity, space and time cease to exist as we know them and current laws of physics cannot be applied to this region.