The debate was about whether media (poetry, plays) should be allowed. Plato thought, no, because poetry and other media burden the audience with emotions that have no value in practical life.
Aristotle countered that the poem has a "payoff" which relieves these emotions generated by reading the poem, so that the audience feels less emotionally burdened by the time it ends.
I particularly like R. G. Collingwood's historical commentary on their debate in The Principles of Art (published 1938), where he talks about our addiction to entertainment and being trapped in a vicious cycle ("one more episode").