Plato wants to banish poets from his ideal republic because he thinks they would distract people from the pursuit of the truth. Poetry makes people emotional, thinks Plato, undermining the full exercise of the soul's rational faculty. And for the arch-rationalist Plato, this is the most important faculty of all. Ultimate truth can only be grasped by the intellect, not the emotions, and poetry leads us astray in this regard.
Plato's understanding of poetry, as with all art, is essentially mimetic. That is to say that he regards the arts as imitating nature. An essential element of Plato's philosophy is that the world around us—the so-called phenomenal world, the world of other humans, animals, plants, and objects—is merely a copy of what is ultimately real: the world of Ideas or Forms.
As Plato believes that poems imitate nature, then they represent nothing more than a copy of a copy. In other words, they are at two removes from what is ultimately real. Poets themselves are therefore not committed to the truth, and so represent a real danger to the stability of Plato's ideal republic. Once the poets have been banished, Plato thinks that society will be more moral, more stable, and more consistently devoted to the pursuit of rational wisdom.