Prose has a few meanings. It is sometimes used to define normal language used in written and verbal communication. In literature, though, prose is typically used to distinguish non-poetry literature from poetry. Whereas poems are often defined by patterns and rhythmic writing, prose is more ordinary writing.
Additional Prose Details
The Merriam-Webster online dictionary has several definitions of prose, including one that defines it as "to write or speak in a dull or ordinary manner." While this definition seems to convey a negative perspective on the writing, it simply means the writing uses plain, simple and easy-to-understand words and phrases. In a story, the writing often more closely mirrors everyday language used in conversation, as opposed to rhyming patterns and schemes in poetry.