Gage R&R (Repeatability and Reproducibility) is a measurement-system analysis that separates true part-to-part variation from variation introduced by the gauge and the operators. Repeatability is variation when the same person re-measures the same part; reproducibility is variation between different people.
You cannot trust capability or SPC conclusions if the measurement system is noisy — a typical rule is that measurement variation should consume less than 10% of total tolerance. Gage R&R is a standard early step in the DMAIC Measure phase.