The quality of your parts largely depends on your machine tool precision. That requires that your machine to have good geometry. Of course nothing is perfect so it is essential to associate numbers to each individual machine on your shop floor, if you are a machine user, or to characterise a machine tool prior to delivery to your customer if you are a machine manufacturer.
The ability of a machine to locate its tool relative to the workpiece directly affects the quality of the machined parts. This ability is quantified by the volumetric errors. The volumetric error varies throughout the machine work envelop as the linear and rotary axes move. The volumetric errors is the result of very small but highly disruptive deviations in the internal geometry of the machine. Some deviations affect the location of successive machine mechanical axes, the inter-axis errors, while others, the intra-axis errors, affect the motion of individual axes. Typically, inter-axis errors are the out-of-squareness and out-of-parallelism between linear and rotary axes, and the linear offsets between the rotary axes including the spindle and tool. As for intra-axis errors, they represent the non ideal motion of each individual machine tool axis. Having quantitative data on those of volumetric errors helps you maintain your part quality whereas knowledge of the contributing error sources helps planning remedial actions to ensure the machine remains accurate.