...namely, striking the ground with the fore foot, not the heel. Watch a video of a toddler running and you'll see they do this naturally. It's only when we start wearing thick-soled, heavier shoes that we re-program ourselves to run differently; heel striking has been linked to knee, hip, and lower back pain.
A commenter wrote that kids should play barefoot to prevent flat feet, mentioning the study "The Influence of Footwear on the Prevalence of Flat Feet" (PDF) from the British Journal of Bone and Joint Surgery:
The distinctly higher incidence [of flat feet] in children who used footwear suggests that shoe-wearing predisposes to flat foot.
Our cross-sectional study suggests that shoe-wearing in early childhood is detrimental to the development of a normal or a high medial longitudinal arch. [...] We suggest that children should be encouraged to play unshod and that slippers and sandals are less harmful than closed-toed shoes.