In Heidegger specifically, authenticity (Erschlossenheit, which does not translate literally as "authenticity") is a technical term refering to when the perceived available life-possibilities coincide with the real available life-possibilities. This is why it is connected to truth, and to death and finitude, and to being-one's-self.
^^^^ CB: May we have an example of a perceived available life-possibility coinciding with the real available life-possibilities ? And an example of them not coinciding ?