Short answers, pulled from the story.
The American system of manufacturing was a set of 19th-century production methods centered on two features: the extensive use of interchangeable parts and mechanization. It enabled semi-skilled labor to manufacture, assemble, and repair complex goods without the hand-fitting required by earlier craft methods.
The system was first fully developed at the United States Armories at Springfield, Massachusetts and Harpers Ferry, Virginia. It was also known as armory practice because of its roots in these government weapons facilities and the private armories that supplied the US Armed Forces.
Mass production using interchangeable parts was first achieved in 1803 by Marc Isambard Brunel, Henry Maudslay, and Simon Goodrich at Portsmouth Block Mills in England, under Brigadier-General Sir Samuel Bentham. By 1808 that facility was producing 130,000 sailing blocks a year for the British Royal Navy.
Eli Whitney is generally credited with both the idea and the practical application, but both are incorrect attributions. He received a US government contract for 10,000 muskets in 1798 based on his reputation as the cotton gin's inventor, but it took him eight years to deliver. He did not express interest in interchangeability until 1800, after Treasury Secretary Oliver Wolcott introduced him to the memoirs of French gunsmith Honore Blanc.
The credit is disputed between Captain John H. Hall, who claimed in a 1822 letter to have achieved it at Harpers Ferry, and Simeon North, a Connecticut arms contractor who invented the milling machine in 1816. Historian Diana Muir argues North has the stronger claim, partly because he worked alongside the Connecticut clock-making industry, the first sector to mass-produce complex machines from interchangeable parts.
The War Department required contractors to open their shops to competitors, and armories shared techniques openly with private industry. Machinists trained in the armory system carried the methods to civilian employers, reaching clockmakers, sewing machine manufacturers including Wilcox and Gibbs and Wheeler and Wilson, and eventually bicycle makers, steam engine manufacturers, and the automobile industry.