Interpretation of the phrase "katharsis of the pathemata" in Aristotle's Poetics has been disputed by scholars since the sixteenth century. The term katharsis in Greek has a sense of purgation or purification. Pathemata means emotions, but in the etymological rather than modern sense, i.e. that they are something suffered or experienced by the person enduring them.
One common interpretation is medical, with the sens eof purgation, Purgatives, which make people vomit, were used in Greek medicine to rid the body of poisons or imbalances. On this reading, Aristotle is arguing that by watching imitation of emotions, we acheive something like apatheia by ridding ourself of excessive emotions.
Another reading is "making the emotions more pure", i.e. training people to have correct emotional responses.