Taylorism was also known as "scientific management." It was an approach to industrial production that emphasized close scrutiny of the production process with the goal of making sure that every step of the process was as efficient as possible.
Frederick Taylor and those who used his ideas would look over the production process in any business. They would look at each step of the process and try to find ways to make those processes more efficient. For example, at one factory, they looked at all the different kinds of things that workers were shoveling. They determined that the different things could be most efficiently shoveled using shovels of different shapes and sizes instead of one standard shovel for all.
Taylorism, then, was the process of using scientific "time and motion" studies to make industrial processes as efficient as possible.