Remember there is 3 main schools of thought regarding the "Singularity" concept, which are more or less compatible.
Accelerating change. Basically Kurzweil's view. Exponential improvement of machines, which will eventually reach then exceed human intelligence in every single domain, or something like that.
Even horizon. If we ever build something that achieve greater-than-human intelligence, we cannot predict whatever it will do to the world, because we're just not as smart as that thing.
Intelligence explosion. If we ever build an AI (or something similar) that is more effective at doing AI research than we are, then that AI would be even more effective… and foom you have something that would leave Skynet in the dust, so it'd better be our friend[1]. Note that the first iteration of that thing may not need to be smarter than us: it just have to be able to build something smarter than itself[2] (and of course, the self-improvement cycle must not hit a ceiling too soon).
Also, we should remind ourselves that we live on a planet with limited physical resources. So, assuming that we build something that could exponentially out-smart us, that thing would still need to have access to physical resources for which what is available on this planet might not just be enough. I see it 2 ways: the thing/it/whatever we want to call it either manages to expand from this planet/solar system before it auto-destroys itself, or it just dies off for lack of available resources.
Accelerating change. Basically Kurzweil's view. Exponential improvement of machines, which will eventually reach then exceed human intelligence in every single domain, or something like that.
Even horizon. If we ever build something that achieve greater-than-human intelligence, we cannot predict whatever it will do to the world, because we're just not as smart as that thing.
Intelligence explosion. If we ever build an AI (or something similar) that is more effective at doing AI research than we are, then that AI would be even more effective… and foom you have something that would leave Skynet in the dust, so it'd better be our friend[1]. Note that the first iteration of that thing may not need to be smarter than us: it just have to be able to build something smarter than itself[2] (and of course, the self-improvement cycle must not hit a ceiling too soon).
[1]: https://en.wikipedia.org/wiki/Friendly_AI [2]: https://en.wikipedia.org/wiki/Seed_AI