The first reason why T. S. Eliot's "Murder in the Cathedral" is called a poetic play is that it is written in poetry rather than prose. There are many other qualities, though, that make it “poetic”.
Drama originally was written in verse. From Greek tragedies through the great plays of Shakespeare, verse was the standard literary form for plays. In the 18th and 19th century, realistic plays written in prose came to dominate the theatre, taking the place of more stylized poetic dramas.
In “Murder in the Cathedral”, Eliot was not only attempting to revive use of verse forms, but also to break away from the predominantly realistic style of his immediate predecessors and revive a more ritualistic and allusive mode of presentation, with language that was evocative rather than purely representational.
Murder in the Cathedral is not a realist play but a meditation on the importance of doing the right thing, even if it means dying for it. Although set in the 12th century (1170) and concerning a real historical event, the murder of Thomas Becket, the archbishop of Canterbury, it was commissioned in 1930s as a commentary on the murderous excesses of the Nazi regime. The play is written in a verse form meant to emphasize the timeless and universal qualities of good and evil, not to recreate a particular historical period.
The play hopes to show that people face the same threats of despotism and the same temptations to protect themselves rather than speak truth to power or stand up for what is right whether it be 1170 or the 1930s. For Eliot, Becket is a model or exemplar of courageous behavior that Eliot hopes others will emulate in the face of Hitler's abuse of power. With its chanting choruses and theme of temptations (bringing us back to Christ in the desert and the timelessness of sin), the play's theme of the timelessness of good and evil is reinforced by Eliot's use of old-fashioned forms of verse.
As an example of Eliot's use of poetry, consider when he has Becket facing a fourth temptation: doing the right thing for the wrong reason, in this case, standing up to the king in order to become a martyr. He uses a rhyming couplet:
The last temptation is the greatest treason: To do the right deed for the wrong reason.
The verse form also reminds us of an earlier, less literate era when people depended on rhyme and alliteration to remember facts and ideas. Eliot likewise wanted his audience to listen to and remember his message about meeting the threat posed by Hitler.