In the real universe, no black holes contain singularities. In general, singularities are the non-physical mathematical result of a flawed physical theory. When scientists talk about black hole singularities, they are talking about the errors that appear in our current theories and not about objects that actually exist. When scientists and non-scientists talk about singularities as if they really exist, they are simply displaying their ignorance. A singularity is a point in space where there is a mass with infinite density. This would lead to a spacetime with an infinite curvature. Singularities are predicted to exist in black holes by Einstein's theory of general relativity, which is a theory that has done remarkably well at matching experimental results. The problem is that infinities never exist in the real world. Whenever an infinity pops out of a theory, it is simply a sign that your theory is too simple to handle extreme cases.