Gravitational Singularity, or spacetime singularity, is a point with infinitely small size and infinitely big density, gravitational force and time curvature. At that point, no physicals laws we know right now can be applied. According to the big bang theory, our universe is expanded from a universe singularity.
According to current theory, when an object falls into the blackhole and approaches to the central singularity of the blackhole, the object will be flattened and elongated because of the larger gravitational force. As it will be longer and longer, the object will finally lose its dimension and disappears at the singularity. Besides, some mathematical inductions state that materials in three dimension world will be destroyed by the singularity and lose its third dimension. Instead it will exist in the blackhole in the form of two-dimensional object, while its two-dimensional data can be restored as three-dimensional object. Therefore, some scientists believe that our world is actually a two-dimensional world, and the third dimension is actually a projection of the two-dimensional data.
Because of the nature of singularity, it is possible that we will never be able to describe singularity with full detail. Nor will we truly understand the singularity in the center of the blackhole. Even though spectator might be able to send signal into blackhole, the spectator might never get any response back. Therefore, we can only induce that singularity do exist by theorems, while we are lack of any data to provide its existence.