Barefoot running shoes are generally considered to be those running shoes that have the most minimal design features and materials that you might as well be running barefoot.
The phrase ‘barefoot running shoes’ is somewhat of an oxymoron as you can’t be running barefoot and in running shoes at the same time, unless you count not wearing socks in running shoes as being barefoot in running shoes!
Having said that, ‘barefoot running shoes’ are generally considered as “shoes” that as close as you can be to being barefoot while still wearing shoes. Barefoot running shoes have minimal design features and minimal materials and next to nothing for the midsole. They are just a covering for the foot, presumably to protect the foot from the environment while still allowing the runners to be as close to being barefoot as possible. As to if these shoes actually achieve that is certainly open to debate and the research evidence is that the running gait in the minimalist barefoot running shoes is slightly different to a true barefoot running gait.
Not all barefoot running shoes would be considered as being “barefoot” or “minimalist” by advocates of barefoot running as many brands and models of these running shoes do have some features added such as, for example, a 5mm stack height for the midsole, which is a lot less than traditional running shoes, but perhaps not close enough to be considered as allowing a barefoot running gait. This just illustrates that across the very wide range of running shoes there are extremes in the different design features that can be used to match up to what each individual runners needs and wants. These range of design features includes the drop (the difference between the heel to toe thickness of the midsole), the stack height (thickness of the sole), flexibility, and motion control features (medial post and rigid heel counter). At one end of the extremes of each of those design features are what would be considered a barefoot running shoe.