Used in Gage R&R studies to indicate a measurement system's ability to detect a difference in the measured characteristic (resolution). You can also think of it as the number of groups within your process data that your measurement system can discern. The Measurement System Analysis Manual published by the Automobile Industry Action Group (AIAG) suggests that 5 or more categories denotes an acceptable measurement system.
Minitab calculates the number of distinct categories by dividing the standard deviation for Parts by the standard deviation for Gage, then multiplies by 1.41. Minitab then truncates this value, except when the value is less than 1. In that case, Minitab sets the number of distinct categories equal to 1. So the number of categories calculated depends on the ratio of the variability in the measured parts and the variability due to the measurement system.
For example, suppose you weigh different chemicals for your batch process. Your formulation requires 4000g of Chemical A, 75g of Chemical B, and 2g of Chemical C. If you use a scale with 5 gram increments for all the measurements, obviously this may be fine for Chemical A, but would not be precise enough for Chemical B and C. Therefore, the scale that measures Chemical A has an acceptable number of distinct categories because the variation in the acceptable weights (3080g - 4020g) is much larger than the variation due to the scale itself.
Typically when the number of categories is less than 2, the measurement system is of no value for controlling the process, because one part cannot be distinguished from another. When the number of categories is 2, the data can be divided into two groups, say high and low. When the number of categories is 3, the data can be divided into 3 groups, say low, middle and high. A value of 5 or more denotes an acceptable measurement system.