'Subject' in epistemology is used to refer to the one who is experiencing. It is often contrasted with 'object'.
The subject may experience and interpret their experiences of the objective realities of the world in a subjective way.
The essence and history of modernity is trying to say that there is a self-certain subject and there is an outer reality and the self-certain subject is engaged in the question of 'What is Reality?', 'What is Truth?', 'What is Knowledge?' or 'What are the premises of my self-certainty?'
This is important because for Heidegger it's the opposite - for him the self-certain subject simply does not exist as given, but is the product of a specific horizon of being, something which is outside or something which is "out there" that first discloses itself to us. It is actually a way of relating to beings in particular which conditions and defines the way in which we come to relate to ourselves.[1]