The singularity is expected to happen when an artificial general intelligence is able to rapidly create more intelligent versions of itself and reach super intelligence.
Initially, we could see the emergence of reversed aging in humans, programmable matter, portable quantum computers, replicators, anti-matter powered spacecraft, and robots that look indistinguishable from humans.
Next, we could see technologies that seem impossible to us now, such as faster than light spacecraft, invisibility suits, holodecks, and black hole computers.
This would be in addition to the increasing use of artificial organs along with nanobots coursing through people's veins to detect and fight cancer and other diseases.
In fact, if there's ever a World War III, super intelligent AIs and other types of AIs could play a more significant role in this war than human soldiers and nukes.