What is the theoretical point of infinite density at a black hole's center?

The theoretical point of infinite density at a black hole's center is called a singularity.

In classical general relativity, a singularity is a place where spacetime curvature becomes infinite and the equations cease to provide a complete physical description. For a simple, non-rotating black hole, the mathematical model places the singularity at a single point. For a rotating Kerr black hole, the model predicts a ring-shaped singularity instead.

The singularity is not the same thing as the event horizon. The event horizon is the boundary beyond which light cannot escape, while the singularity is the predicted central region inside that boundary. An accretion disk is hot, orbiting material outside the horizon, and an ergosphere is a region outside the horizon of a rotating black hole where spacetime is dragged around.

Physicists generally treat infinite density as a warning that classical relativity is incomplete under such extreme conditions. A future theory of quantum gravity may replace the singularity with a different structure, so the word describes the prediction of current mathematical models rather than a directly observed point of infinite density.