Explain the mimetic theory in Plato's Republic X ?
This a great question. Plato's theory of mimeisis is central to his theory of the forms. Mimeisis can be thought of imitation or mimicry. Nature imitates the forms, which according to Plato are unchanging, eternal, and perfect.
For Plato the danger is that people imitate what is not good. This is why Plato exiles poets from his ideal republic. In Plato's mind, poets are not philosophers. So, they do not know the forms. For this reason, their works are imitations of the forms (usually base imitations). When people, who are not philosophers as well, see these plays being done (such as Greek tragedies), they imitate what is not true. This, in turn, strengthens the apetitive part of a person, which is the basest part of a person within Plato's theory of the tripartite soul of a person.