runout is a machinist's term for eccentricity perpendicular to a rotating axis.
In short, visualize a loaded cartridge held and spun on it's long axis in a precision fixture. A dial indicator measuring tool is used to measure how much it is out of "perfect" rotation from that axis. That measurement is runout.
These measurements are important to the precision shooter (competition, varmint, long-range, etc) in getting perfect ammunition.
HTH
John