A singularity is a place where the curvature of spacetime becomes infinitely great and the known laws of physics no longer apply. It is where, as the Caltech physicist Kip Thorne (1940–) colorfully described it, gravity "unglues" space and time.
Singularities may be points, one-dimensional lines, or even two-dimensional sheets. The general theory of relativity predicts that singularities form inside black holes but are concealed from the rest of the universe behind event horizons. A proper formulation of quantum gravity may well avoid the infinities associated with classical singularities.
In mathematics, a singularity is a point at which a curve, function, or property behaves unusually, e.g., by having a node, cusp, or an isolated point.