A dramatic verse is a type of poem that is used to tell a story. Many stories were told with the use of dramatic verse most of Shakespeare's work, for example. A dramatic verse poem does not have a specified structure. It is simply a verse with a dramatic flair and tale to tell. It was once the preferred way to tell a dramatic story and is still widely enjoyed.
A tragedy is generally the genre of the poem that a dramatic verse is used to portray. This is due to the serious nature that a tragedy demands. Originally, a dramatic verse was used to tell such tragic and dramatic tales because prose of a verse is easier to memorize and retain. This allowed people to share the stories that they enjoy and wish to use to entertain an audience with relative ease. A dramatic verse will more likely than not consist of extraordinary feats, myths, and more.
Any drama written as verse to be spoken; another possible general term is poetic drama.