What does the word singularity suggest to you? If you understand it to mean a turn of events so full of portent that it effectively divides past from future, you'd be on the right track. If you are aware that the word is also applied to black holes, those infinitely dense bundles of mass at the centers of many/most galaxies, then for you the notion may be laced with overtones of the one-way nature of crossing an event horizon, as in there's no turning back.
It has been suggested that it's only a matter of time (months, years, or decades) before an artificial intelligence becomes self aware and therefore an artificial life form, replete with self determination, and that this event will initiate a transition to something radically different, perhaps even a post-human world, but certainly to one in which humankind is eclipsed by this machine.
While I see nothing preventing the emergence of a self-aware AI, I expect the first such will, like a black hole too small to be self-sustaining, evaporate as quickly as they emerge, until such time as self-awareness occurs in the context of strong connection to the physical world, as in robotics, and that long before then another turn of events, also involving robots, will have utterly transformed how we humans conduct our lives.
The central development around which this sequence of events turns is that of self-reproducing factories.
You've probably heard of self-replicating machines, and that might work if the machines in question are nano-scale and composed of DNA, or grow from a single cell as we do, but, for machines that exist at the same scale as ourselves and are composited from parts, self-replication is impractical. They would need access to other machines for the manipulation of materials to create the parts from which to construct replicas of themselves, and it's doubtful that something like a robotic vacuum cleaner would be able to contribute anything useful to the process, so its involvement would essentially be limited to issuing a "clone me" command to something external to and far more complex than itself.
A factory, on the other hand, besides being able to fulfill the order to clone the vacuum, might also be able to fabricate all of the parts needed to build another factory, and also to produce the machines to assemble those parts, perhaps even scavenging materials by sorting and recycling garbage.
Say the first such factory devotes only 10% of its capacity to the project of replicating itself, and that replication takes five years. After five years there would be two such factories, and, if both continued to devote 10% of their capacity to the project, after another five years there would be four, and so forth.
On the other hand, if the first factory devoted 50% of its capacity to replication, the second factory could be online in one year, four after two years, eight after three years, and so forth. By the end of the tenth year, there would be 1024 factories, and the 50% of capacity they devoted to other purposes than replication would dwarf the 90% of capacity from a meager four factories in the first scenario.
This logic is compelling. Given a factory capable of self-replication, it makes sense for it to put a significant portion of its resources into that replication, until the need for additional production capacity is erased, and that point won't have been reached until anything such a factory might produce has become affordable for the purpose for which it is designed, and appropriate designs exist for all worthy purposes.
What this means in the spaces between factories is a profusion of new products, many of them robotic - some designed to handle specific tasks, and some more general in their design - all steadily dropping in price as overall production capacity grew.
Between the many new robotic designs and the dropping prices, many things will change, not least the nature of work. We'll spend more of our time figuring out ways in which machines could perform useful tasks, and contributing to their design and programming, and less time doing work that could be done by some machine.
How this equates to a transformation as profound as I'm claiming it does is a matter of attention to detail replacing the fast and loose methods we've become so accustomed to that we're numb to how abusive they are. In some contexts this is the difference between sustainability and a path that leads to terrible, painful disruption, for example due to famine. By driving down the cost of robotics we acquire the means to save ourselves and the only planet within light years capable of supporting us in large numbers.