"It was clear to me that the forms of consciousness of our inherited and acquired historical education - aesthetic consciousness and historical consciousness - presented alienated forms of our true historical being"

This quote by Hans-Georg Gadamer is describing the concept that the forms of awareness that we have actually inherited and gotten via our education and learning, such as aesthetic consciousness as well as historical awareness, are not necessarily reflective of our true historical being. Simply put, these types of awareness are not always reflective of our real identity as well as our true background. Rather, they are kinds of consciousness that have been imposed upon us by our education and learning and also our society, and they are types of awareness that have actually been estranged from our real historical being. This quote is suggesting that we need to be aware of the types of awareness that we have inherited and gotten, which we should aim to reconnect with our true historical being.