Some examples of non-prose materials include poems and songs. Generally speaking, anything that uses a proper sentence and grammatical structure can be considered prose, and anything that does not can be considered non-prose.
The word prose comes from a 14th century French word that means "story" or "narration". That itself is derived from the Latin words prosa oratio, which means "straightforward or direct speech." The term applies to all writings that follow the standard writing and grammatical format: punctuations, sentences and paragraphs. It emulates ordinary speech and flows without any specific accents or rhythm. Novels, essays, short stories and speeches are all examples of prose writing.
Works that are not prose usually fall into the verse category. Verse writings follow a unique scheme, usually with a rhythmic pattern and rhymes. Unlike prose, verse writings can be manipulated by the author to give off an intended effect. For example, sentences can be cut off prematurely, words can be given emphasis, and punctuations can be used in areas they would not usually go, or sometimes not used at all. Some examples of verse writings include songs, lyrics, and poems.
The works of Shakespeare are well known for their inclusion of both prose and verse. His writings are great resources to look at for examples of both.