Narrative poems tell stories. They follow the same structure of a short story. Narrative poems can be long or short and simple or complex. They also use the same literary devices like a plot and character as would be found in a short story. Rhyming couplets, alliteration, repetition, and so on, are used too.
Excerpt from The Raven by Edgar Allan Poe
Once upon a midnight dreary, while I pondered weak and weary,
Over many a quaint and curious volume of forgotten lore,
While I nodded, nearly napping, suddenly there came a tapping,
As of some one gently rapping, rapping at my chamber door.
"'Tis some visitor," I muttered, "tapping at my chamber door -
Only this, and nothing more."