What is a barefoot shoe?

A barefoot shoe is simply a shoe that allows the foot to function fully as it should.
A barefoot shoe will have all or most of these characteristics.

Zero drop. This refers to the amount of elevation from heel to toe. Specifically no elevated heel.

A wide toe box. Enough room to allow full toe splay. The big toe and the pinky toe should have enough room without being pressed against the sides.

Flexible. Bendy and should be able to mostly be able to fold in half both upwards and downwards as well as the ability to rotate, similar to the way the foot should function.

Thin sole. The thinner the sole, the better the ground feel of the floor and the world around us. This trait will differ most based on brand and preference. The closer it is to barefoot the better for the maximum benefits.

Zero toe spring. This refers to an elevated toe box which can slightly push your toes up in a extended position. 

Zero arch support. Specifically no support or any sort of elevation in the sole especially in the middle.

Attached to the foot. Both the front and back of shoe should be attached to the foot to allow maximum function and gait mechanics.