The evolutionary hypothesis proposing rapid bursts of change separated by long periods of stasis is punctuated equilibrium. It was introduced in 1972 by paleontologists Niles Eldredge and Stephen Jay Gould.
The idea emerged partly from gaps and patterns in the fossil record. Instead of assuming that species always transform gradually and continuously, punctuated equilibrium proposes that many species remain relatively stable for long intervals, then undergo comparatively rapid evolutionary change, often around speciation events. In geological terms, “rapid” can still mean thousands of years.
Punctuated equilibrium is commonly contrasted with phyletic gradualism, which portrays evolutionary change as slow and steady within a lineage. The hypothesis does not claim that every species evolves in sudden bursts, nor does it reject natural selection. Rather, it emphasizes that evolutionary rates can vary and that speciation may be concentrated in relatively short periods.
The term is sometimes confused with “gradualism,” but gradualism describes the alternative pattern of continuous change. Darwinian evolution is a broad framework, not the specific hypothesis named in this question.