The word singularity comes from math where it means a part of a graph where a function becomes discontinuous (i.e. the value of the line at that point is either undefined or infinite). Things like evolution, immortality, and fusing together into a hive mind have nothing to do with it, at least not inherently.

The idea of the technological singularity comes from the observation that the rate of new technological advances is becoming faster over time such that our total level of technology is growing hyperbolically. If human technology continues growing at the current hyperbolic rate or something close to it then relatively soon we will reach the singularity on the graph of new technological innovations which is the point in time where the rate of new technological innovation will become infinite.

The general assumption of this subreddit is that the technological singularity occurs as the result of the creation of a self improving AI which will then proceed to rapidly create better and better versions of itself. The hope is that if AI is controllable or at least benevolent it could bring about a golden age where all science is known and essentially all economic activity is automated.