Definition of Resolution:
Resolution is a measure of the degree of confounding among effects. Roman numerals are used to denote resolution. The resolution of your design defines the amount of information that can be provided by the design of experiment. As with a computer screen, the above is an explanation of resolution in the context of DOE.
For Gage R & R, ‘Number of distinct categories’ measures the ability of the measurement system to resolve the data in to a number of catogories – hence a measurement of resolution – the greater, the better.