Short answers, pulled from the story.
Interchangeable parts are components made to such precise specifications that any one of them can replace another of the same type without custom fitting. They make assembly and repair faster, cheaper, and less dependent on highly skilled labor, and they were crucial to the introduction of the assembly line at the beginning of the 20th century.
The earliest known use dates back over two thousand years to Carthage during the First Punic War. Carthaginian warships carried standardized, interchangeable parts that even came with assembly instructions marked on them.
Mass production using interchangeable parts was first achieved in 1803 at Portsmouth Block Mills in Portsmouth Dockyard, England. Marc Isambard Brunel, Henry Maudslay, and Simon Goodrich, working under Brigadier-General Sir Samuel Bentham, built 45 machines that produced pulley blocks for the Royal Navy, reaching 130,000 blocks per year by 1808.
Eli Whitney did not actually achieve true interchangeable parts manufacturing, despite his famous 1801 demonstration before Congress. Historians Merritt Roe Smith and Robert B. Gordon determined that his guns were costly and handmade by skilled workmen. Whitney's family arms company achieved genuine interchangeability only after his death.
Eli Terry was using interchangeable parts with a milling machine as early as 1800, making wooden clock components in batches using jigs and templates. In 1806 he signed the Porter Contract to produce 4,000 clocks in three years, the first mass production using interchangeable parts in America, entirely without government funding.
The Systeme Gribeauval was a French military standardization program issued as a royal order in 1765, promoted by General Jean-Baptiste Vaquette de Gribeauval. It focused mainly on artillery and introduced precisely bored cannon barrels that allowed thinner walls, shorter barrels, and standardized shells. It also provided patronage to Honore Blanc, who by around 1778 was producing muskets with interchangeable flintlock mechanisms.