Hamlet states that the purpose of drama has always been "to hold, as 'twere, the mirror up to nature; to show virtue her own feature, scorn her own image, and the very age and body of the time his form and pressure". What does Hamlet mean by these words?

I think Hamlet is referring to truth. So many times the truth becomes distorted, even within a seemingly authentic emotion or virtue. It is the job of true drama to be authentic to its own motivations. The meaning behind the drama is unfolding must remain true to what it is.