Tolerances control the dimensional accuracy of a bearing.
ISO bearing tolerances start at P0 and then move upwards to precision grades P6, P5 and then P4. ISO tolerances are measured in thousandths of a millimetre (or microns). AFBMA (ABEC) bearing tolerances are also commonly used and these are measured in ten-
Assuming that the shaft and housing are manufactured to the same tolerances as the bearing, tighter bearing tolerances will improve mating between shaft/housing and bearing, noise/vibration levels and starting/running torque.