An autapomorphic trait is one that is found in one and only group. Wikipedia gives the following definition: an autapomorphy is a distinctive anatomical feature, known as a derived trait, that is unique to a given terminal group.
The autapomorphic species concept is one of 26 ways scientists have used to distinguish species from each other.
Autapomorphy has been applied to studies of human evolution where Kennedy (1991) found that on this basis of discrimination Homo erectus could not be considered a distinct species.
Paleotologists will use autapomorphic traits to help identify new species found through fossil discovery.
Farke, A. A., & Sertich, J. W. (2013). An Abelisauroid Theropod Dinosaur from the Turonian of Madagascar.Plos ONE, 8(4), 1-18. doi:10.1371/journal.pone.0062047
Kennedy, G.E., (1991). On the autapomorphic traits of Homo erectus. Journal Of Human Evolution, 20, 375-412. doi:10.1016/0047-2484(91)90006-H