Authenticity is hard to define but you know it when you see it. Roughly speaking, it is the opposite of imitation. The Kotzker was a great fan of authenticity, as in the following vort:
The gemara says that "many did as Rabbi Shimon bar Yochai did [devoting himself solely to the life of the spirit] but did not succeed". The Kotzker asks why they should not succeed since surely that path is a meritorious one. He answers that imitation -- even of one as worthy as Rabbi Shimon bar Yochai -- just doesn't cut it (nokhgemakht toigt nisht).

The quest for authenticity is generally regarded as a modern phenomenon and is not without its critics. Critics on the right equate authenticity with self-fulfillment and see the quest for authenticity as a threat to the social order. Critics on the left regard the very notion of identity as an artificial construct and so view the possibility of authenticity as a chimera. (They're just a bunch of nisht farginers. If you're sufficiently self-aware that they can't patronize you, you must be possessed of false consciousness.)

Many early chassidishe thinkers were keenly sensitive to the dual threat posed by the quest for authenticity: subversion of social order and false consciousness. The Pshischa (I don't give a damn how the Polaks spell it) line, which reached its apotheosis with the Sfas Emes, does not sweep either of these problems under the rug. But everything gets neatly tied up with the following argument: the only true identity is one that radiates out (albeit differently for different people) from an internal point (nekudah pnimis) which yearns for dveikus with its creator. So, indeed, what passes for authenticity is in fact fake unless it is rooted in a yearning for dveikus which can only be realized through Torah and mitzvos. (George Costanza: Do you ever yearn? Jerry Seinfeld: No, but I sometimes crave.) Thus the true quest for authenticity is subversive only of bourgeouis pretense but not of Torah. Convenient, eh?