What is a singularity? It’s when a large number or set of things converges to a single value that is often a type of infinity.  In mathematics a singularity is often when a function becomes undefined because the result is both positive and negative infinity. The classic example is the function of y = 1/x, but when x gets closer and closer to zero it tends to infinity.

Technological Singularity

Sometimes in technology, a singularity is defined as a point at which technologies have the ability to intelligently manipulate energy and matter with essentially one device. The idea is that as technology progresses it tends to improve exponentially. 


How a technological singularity might progress. image: Myworkforwiki /wikipedia

There is no real consensus on what the exact nature of technological singularity might be.  For example there is some suggestion that it means artificial intelligence (AI)  that is far superior to human intelligence to the idea of convergence of everything into one kind of super brain. 

Gravitational singularity

This is more a classic singularity which describes the state of matter at the centre of a black-hole tending towards infinity. The current laws of physics break down and new kinds of physics may need to be developed to describe the situation. This may also apply to the beginning of the universe using the Big Bang Theory. 


A two dimensional embedded diagram of a black hole.