Indexing in reference to motion is moving (or being moved) into a new position or location quickly and easily but also precisely. After a machine part has been indexed, its location is known to within a few hundredths of a millimeter (thousandths of an inch), or often even to within a few thousandths of a millimeter (ten-thousandths of an inch), despite the fact that no elaborate measuring or layout was needed to establish that location. Indexing is a necessary kind of motion in many areas of mechanical engineering and machining. A part that indexes, or can be indexed, is said to be indexable.
Usually when the word indexing is used, it refers specifically to rotation. That is, indexing is most often the quick and easy but precise rotation of a machine part through a certain known number of degrees. For example, Machinery's Handbook, 25th edition, in its section on milling machine indexing, says, "Positioning a workpiece at a precise angle or interval of rotation for a machining operation is called indexing." In addition to that most classic sense of the word, the swapping of one part for another, or other controlled movements, are also sometimes referred to as indexing, even if rotation is not the focus.
There are various examples of indexing that laypersons (non-engineers and non-machinists) can find in everyday life. These motions are not always called by the name indexing, but the idea is essentially similar:
Indexing is vital in manufacturing, especially mass production, where a well-defined cycle of motions must be repeated quickly and easily—but precisely—for each interchangeable part that is made. Without indexing capability, all manufacturing would have to be done on a craft basis, and interchangeable parts would have very high unit cost because of the time and skill needed to produce each unit. In fact, the evolution of modern technologies depended on the shift in methods from crafts (in which toolpath is controlled via operator skill) to indexing-capable toolpath control. A prime example of this theme was the development of the turret lathe, whose turret indexes tool positions, one after another, to allow successive tools to move into place, take precisely placed cuts, then make way for the next tool.