The point at which something peculiar happens to an equation (or the physical process represented by the equation).

The point where one or more variables in the equation have certain values.

If you toss a ball vertically into the air it reaches a singularity at the top of its path because at that point the velocity is zero.

In special relativity no object can go faster than light because at that speed the equations for length, time and mass have singularities as length becomes zero, time stops and mass becomes infinite. (see Length Contraction and Time Dilation)

According to some theories, there exists a singularity at the centre of some Black Holes.