The term "radial run-out" refers to a situation where the tire radius fluctuates from the wheel midpoint. In other words, the radius is not uniform from the center to any point on the rim of the tire.
Any rotating shaft is likely to be less tolerant to radial run-out because the amount of run-out dislocates the center of gravity. When it comes to vehicles, too much radial run-out in tires might induce up-and-down vibrations, resulting in hopping. This malformation of the tires/wheels is one of the major reasons behind bumpy rides and even collision in severe conditions.