What does singularity mean in the context of black holes?

Question

Non-rotating big stars can be subject to a gravitational collapse increasing their density. When the density is so high that the mass volume shrinks below the event horizon, a black hole is formed.

Is such an "initial" black hole already considered as a singularity, or are there further shrinking processes required in order to consider the black hole to be a singularity? Do the characteristic dynamics of black holes include further shrinking processes until the mass is reduced to a point (or nearly)?

Answer 1

A singularity is defined as a point of infinite density and they are believed to reside at the center of a black hole .

The "when does the singularity form" question, is answered concisely here.