I believe the word singularity has a more rigourous definition. IANAP, but I believe singularity in physics refers to either time 0 where backwards extrapolation divides by zero, or the similar problem trying to calculate what happens inside a black hole. You literally lose the ability to predict what happens.
Thus it is with social singularities. The social change is so profound that you cannot predict what will happen. No one could have predicted the changes the printing press made in Europe, with growing literacy and democratization of governments. No one could have predicted the changes wrought by electronics / computers / the internet. No one can predict what will happen when computers achieve human equivalent intelligence, and shortly thereafter superhuman intelligence in accord with Moore's law.
Think of it as a phase change. People whose weather experience is limited to temperatures of 30-40C normally and 20C once in a blue moon would imagine 0 to just be more so, possibly uncomfortable. Snow and ice would be utterly foreign to them, unimaginable and unpredictable.