Definition: In scientific terms, a gravitational singularity (or space-time singularity) is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system.
What is a singularity in physics?
A singularity means a point where some property is infinite. For example, at the center of a black hole, according to classical theory, the density is infinite (because a finite mass is compressed to a zero volume). Hence it is a singularity.
What exactly is the singularity?
In the center of a black hole is a gravitational singularity, a one-dimensional point which contains a huge mass in an infinitely small space, where density and gravity become infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate.