Precision goes back quite far. A Geneva clockmaker of 1750, working with calipers, dividers, pretty simple man-powered lathes and gear-cutting engines, and hand tools like scrapers, files and abrasive stones, could make clocks with very fine tolerances, easily + - .001"/.025mm. And a kind of mass production was not unknown, either. A Geneva watchmaker could be buying cases from a case maker who'd be supplying many watchmakers. Some pre-industrial crafts would also maximize their production with economies of scale ( having a big shop doing a lot of work) and specialization. A musket made circa 1720 would have a barrel made by specialists who did nothing but weld, specialists who would grind, and specialists to ream and finish gun barrels: and other components, like the brass triggerguards and flintlock mechanisms, would have their own specialists.

However, a very big leap came with the development of energy sources ( both steam and water power) and machine tools that made possible repeatable operations: the Geneva watchmaker could fit parts together with high precision, using handtools, but he would not have a machine lathe and a micrometer to let him turn out pivots at exactly 1.25 mm diameter. That really came in with the English industrial revolution, especially in the shop of Joseph Bramah and the inventions of Henry Maudsley, circa 1800. Maudsley developed a number of precision lathes, milling machines and precision measuring instruments that enabled Bramah to greatly increase his production of his new padlocks.

Another advance came from the American effort to make firearms with interchangeable parts. This was an idea that Thomas Jefferson brought back from his tour of a French armory, and it was first implemented in the shop of John Hall at the Harper's Ferry Arsenal in 1819. Hall was making a breech-loading rifle that required many more metal-working steps than a regular rifle, and working with machine lathes, milling machines, and special gauges, jigs, and fixtures he was able to turn out parts that were uniform enough to require very little fitting. This idea of repeatable operations creating uniform parts was then often called the American System, and would be taken up by other armories in the world as well as makers of machines like grain harvesters and sewing machines.

Hounshell, D. (1984). From the American System to Mass Production, 1800-1932: The Development of Manufacturing Technology in the United States (Studies in Industry and Society) (First Edition (US) First Printing). The Johns Hopkins University Press.