That rapid progression can be modeled with an exponential growth curve, like Moore’s law, even though nothing material can have a sustained exponential growth. Regardless of how the curve is modeled, the steepness is such that it serves as a step function in evolution.
With that clarified, there is first the question of “is the technological progression going to level off soon?” And I think the answer is no. The second question is, “how are we going to deal?” And the answer to that question can only be addressed once we answer the question: “what kind of world do we want to live in?”
People generally use the term to mean the point at which progress is automatic, unbounded, and instant. E.g. AIs that can produce smarter AIs themselves, in short order.
I’m not a singularity believer (singularitist?); from the perspective of 1000 years ago we’re already at the point of infinite progress in zero time. I think individuals, the culture, and the species adapt to accelerating progress, and I intuit, maybe wrongly, that Gödel‘s theorem means that technology will never become runaway and recursive.
But I think that’s what people mean, more than just a step/paradigm change like the internet.