The term "American system of manufacturing" is usually used to refer to a process that broke down the process of manufacturing into steps that could be done by relatively unskilled workers. One of the most important aspects of this was the development of a process for making interchangeable parts.
The American system did away with a system where skilled labor made all the parts for an individual machine. The parts for one machine would not fit another and the worker had to be skilled. In the American system, all the parts were made by a machine tool to be relatively identical. Any piece could be put into any machine, meaning that an assembly line process was possible. Running the machine tools was much easier than making parts so less skill was needed.
For these reasons, the American system was more efficient and could make products faster and more cheaply than previously possible.