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What did Thomas Kuhn mean by incommensurability between paradigms?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Philosophy of science Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

In the philosophy of science, Thomas Kuhn used the term incommensurability to describe the fundamental disconnect between competing scientific paradigms. Drawing on a mathematical metaphor regarding numbers that share no common measure, Kuhn argued that when one paradigm replaces another during a scientific revolution, they cannot be directly compared or translated.1

Kuhn identified three primary aspects of this incommensurability:

Conceptual: The languages used by different paradigms are not readily translatable. Terms often shift in meaning, making communication between proponents of rival paradigms partial or difficult.1
Observational: Scientists working within different paradigms may perceive the world differently, even when observing the same phenomena. They essentially "see" different things because their observations are filtered through their respective theoretical frameworks.1
Methodological: Paradigms possess different criteria for success, valuing different types of questions and evidence. There is no neutral, objective standard to weigh the virtues and defects of competing approaches, which challenges traditional views of scientific progress as a purely rational, cumulative process.1

Ultimately, Kuhn suggested that these differences are so profound that scientists operating under different paradigms effectively work in "different worlds".1