Prose is any kind of text that is written with standard grammatical structure and generally flows naturally, as regular speech. It is meant to be straightforward and clear, and is typically used in publications such as newspapers, magazines, essays or journals, and even some literature. Prose is written to inform, entertain, or persuade. In terms of form, it is basically anything that is composed of sentences.
Poetry, however, is composed by the line. This written form has many variations, but is often made apparent by a particular structure in grammar, language, rhythm and meter, or literary element. Poetry possesses a deeper meaning and often requires analysis to understand. Poems are used in plays or dramas (such as those by Shakespeare), some literature, and songs or lyrics, and are often published in anthologies or literary magazines dedicated to the art form. Poetry is intended to evoke an emotional response from the reader.
Poetry and prose are considered the two only forms of writing. In other words, anything that is not poetry is prose.