When you move with shoes on you are forced into a heel strike, which then forcefully clomps the toe to the ground (known as "clomping"). Your foot stays flat on the ground longer increasing the load forces into the ground & into your body. The shoe "rocks" your foot forward which results in little or no pushoff the ground.
When barefoot, you contact the ground lightly on your midfoot. Your foot then rolls naturally through an "S" motion path, which dissipates load forces. Finally, when your heel lifts up your toes & arch muscles are pre-stretched resulting in a thrust pushoff the ground.