Orthopedic Perspective
The foot, when bare, naturally lands more in the middle or "mid-foot" much like an ice skater lands while gilding along the ice. This eliminates the popular concept of 'heel strike' when walking as the correct gait. With this change in foot placement, the intrinsic muscles of the foot are capable of working which in turn builds natural strength to the muscles of the foot.
With shoes we change the way the foot lands, and is used. Some muscles important in protecting the foot 'turn off' or are not being used because of the change in gait. This creates muscle weakness. Also when wearing shoes, the foot is more rigid and unable to yield and absorb the body weight as it transfers over the foot. These muscles inside the foot (intrinsic muscles) are unable to assist in the impact of the weight which is what they are designed to do. The feet need to do their natural "weight workout routine" and by being barefoot they can do so and act as the body's natural shock absorber and get stronger because of it.