The whole topic of sports equipment, sports health, and sports injuries is one in which the scientific quality of most of the information tends to be extremely poor. However, there is a group at Harvard that does research on barefoot running, and they have a [web page][1] with a lot of good information on it.
As far as I've seen from browsing through their materials casually, it seems like one argument in favour of barefoot running is the following:
When you get injured, it isn't just the amount of force that determines the damage, but also the rate at which the force changes, i.e., how "jerky" it is.
If you know calculus, this is a statement that the third derivative of the position with respect to time is important. This is pretty well understood for machines, and probably applies to the human body as well. For example, a machine like a mill or a lathe can be damaged by vibration, and you can't make the machine vibrate by using a steady force, only by using a force that changes rapidly.
The Harvard group has data showing that shod runners have more "jerky" impact with the ground and, like machines, are more prone to vibration damage or injury.
There is also evidence that the factors you'd think would affect injury, such as cushioning and distance, actually don't have much effect, because people subconsciously adjust their bodies. However, these subconscious adjustments may make barefoot runners [less efficient][2].
Some other info:
http://articles.latimes.com/2013/jun/27/news/la-sn-ultra-marathon-20130627
http://www.nytimes.com/2011/06/21/health/nutrition/21best.html?_r=1&ref=science
http://well.blogs.nytimes.com/2013/06/26/the-myth-of-pronation-and-running-injuries/?smid=pl-share
http://www.runresearchjunkie.com/just-how-significant-are-heel-impacts-at-causing-injury-when-running/ [1]: http://barefootrunning.fas.harvard.edu/ [2]: http://well.blogs.nytimes.com/2012/03/21/making-the-case-for-running-shoes/#
