A singularity contains the entire mass of a collapsed star in a single indefinitely small point. It is a point of infinite density and gravity, causing the known laws of physics to break down. This center point of gravitational force is what causes the surrounding black hole and resides in the center of every black hole. At the singularity, the laws of physics break down and become unpredictable. The immense gravity warps four-dimensional spacetime into a single dimension. This means that objects falling into the black hole can only move toward the singularity, and time does not exist for them in a recognizable form.
A singularity has never been observed, so while it could be mathematically or theoretically true, it can't be confirmed. The event horizon of a black hole, the boundary that light cannot pass out of, surrounds the singularity, so no information can escape from the singularity. Therefore we will never be able to see a singularity or observe it, and cannot know that it exists.
[P1] A black hole forms when lots of mass collapses into a very small point. [P2] This point, the singularity, has infinite gravity and density. [P3] Because of the singularity's immense gravity, spacetime is warped into a single dimension at the singularity.