What is, according to Hamlet, the purpose of drama? And what does Hamlet most admire about Horatio?

Expert Answers
teachersage eNotes educator| Certified Educator

Hamlet lectures the players on realism in acting and theatre. While speaking in general terms about the purpose of drama, he states it should be a mirror of the actual world. Drama's point has always been ("first and now") to show audiences what goodness ("virtue") really looks like and also to show what nastiness ("scorn") is really like, as well as to show the larger society what it is like ("the very age and body of time his form"). As he puts it:

For anything so overdone is from the purpose of playing, whose end, both at the first and now, was and is 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.

(It is worth noting as an aside that if drama's purpose always is to mirror to the larger society what it is really like, Hamlet is making a scathing commentary on the corruption of life in the England of Shakespeare's day.)
However, while the players believe Hamlet is simply communicating to them his theory of acting, we as an audience know his underlying agenda: Hamlet wants the play to be as like real life as possible to represent to Claudius his own possible crime of murder so vividly that he is startled and reacts. From this reaction, Hamlet hopes to be able to gauge Claudius's guilt or innocence. 
Hamlet especially wishes Horatio, who has seen the Ghost and knows what is going on, to watch Claudius carefully, because he, Hamlet, admires Horatio's level-headedness: Horatio is the essence of the rational, not the emotional, man. Hamlet states to him:
Give me that man
That is not passion’s slave, and I will wear him
In my heart’s core, ay, in my heart of heart,
As I do thee.
This shows not only Hamlet's own affection and admiration for Horatio but an awareness of the extent to which his own emotions might color his interpretation of events and how important it is to have a second pair of eyes he can rely on to verify whatever he thinks he sees. 
ms-mcgregor eNotes educator| Certified Educator

In Act III, scene 2, Hamlet is giving advice to the players who are about to perform "The Murder of Gonzago". He says the purpose of drama is to imitate life. He has cautions the players not to be too "tame" or to "overdo" their actions because "the purpose of playing, whose end, both at the first and now, was/ and is, to hold, as 'twere, the mirror up to nature...".( III,ii,19-20) In other words, the purpose of acting and, therefore drama, is to come as close to reality as possible. A little later, he praises Horatio for being an "even" or not battered by his emotions. He says, Horatio, "thou art e'en as just a man
As e'er my conversation cop'd withal. ( III,ii,49-50)
Horatio is a little embarrassed by the compliment but Hamlet goes on to say,"Give me that man/ That is not passion's slave, and I will wear him/ In my heart's core, ay, in my heart of heart,/As I do thee."
( III,ii, 67-70) In other words, Horatio is not a slave to his emotions and that is what Hamlet admires in him.