Big question. I'll talk about only a couple general things.
In the Poetics, Aristotle describes mimesis as imitation: mimesis can only produce certain features of its object.
Plato's doctrine on mimesis was a bit more pejorative, saying that poets tried to communicate truth through their tales, but were so far removed from the truth. Plato thought only philosophers could attain truth in this way. He used the trio of the Ideal Bed (the perfect conceptual bed), then the carpenter's bed and finally the painter/artist's depiction (imitation) of the bed, this last one being the furthest from the truth.
Aristotle paints a bit of a different picture of mimesis. He talks about how mimesis is a natural human technique: children learn by imitating. We imitate words in order to communicate using the same language. Art that is most mimetic is closest to the real thing. For Aristotle, music is the most mimetic. He felt that visual arts were more indirect/less mimetic.
With plays, Aristotle thought the catharsis experienced by the audience would be good. This is a bit of a twist on his philosophy of mimesis. A successful play will be mimetic but paradoxically: the audience will be affected (he says by fear and pit - and maybe empathy) but for two oppositional reasons: the audience will identify with characters and their tragedies and feel for them but the audience, knowing the play is just a representation, will feel relieved that the play is simulation and their lives are real. So the play must be mimetic (real enough to be affecting) but its success also implies that the audience can distance themselves from the play. The separation between art and life.
One more quick thing: Aristotle also talked about technique (jobs) and their relation to nature. Technique/nature is congruent to Art/Life. Humans use medicine as a way to mime nature and its creation of life/health. But using medicine (technique) is a bit different because medicine and nature seek the same ends and because practicing medicine supplements nature (does what nature can't). So, here, mimesis is not just simulation for simulation's or education's sake.
Aristotle's mimesis philosophy is somewhat of a response to Plato's ideas so there are differences and similarities. One of the big ideas with Aristotle's mimesis is that, whatever the medium, the audience can take pleasure in mimesis because they are not fooled by it: in other words, it must appear real enough to affect intellect and emotion, but fake enough to be clear that it is just imitation.