A Heideggerian term, authenticity is a mode of Dasein (identified as the individual's "being there"; it is the human being, or existance of human beings, or existents1). Among all possible modes available to Dasein, Heidegger presents the authentic as the only one which enables us to come into and cultivate our own individuality. Authenticity involves living up to one's full potential, and not falling prey to the homogeneity and inauthenticity of the public sphere (also identified as the They). This happens when one becomes preoccupied with generalities, every day preoccupations and trivial pursuits (pardon the pun); furthermore, one falls away from authenticity by identifying oneself as a token of a type ("I am a doctor/ student/grandmother/vegan social activist") rather than a unique being. Of course, it is difficult to imagine ever fully escaping from using these sorts of signification in our everyday public discourse, but it is possible to oscillate between these two modes in such a way that while we are immersed in the public world, we do not lose sight of our individuality permanently.

In a nutshell: authenticity, as a mode of Dasein, represents a concern and care for self that focuses on the intrinsic individuality of each human being as he or she goes about the act of living.

1I realize that "existents" refers to beings in general, but I felt that for the sake of contrast, it was okay to use it that way.