The main difference between the different forms of literature is the purpose and the way words are arranged.

The main difference between prose and poetry is how the words are used.  In prose we form words into sentences and paragraphs.  In poetry we form words into lines and stanzas.  Many of the rules of punctuation and grammar apply to poetry, but the poet can choose to change them as he or she wishes.  Here is an example from ee cummings.

somewhere i have never travelled,gladly beyond
any experience,your eyes have their silence:
in your most frail gesture are things which enclose
me,
or which I cannot touch because they are too near

You can see that the poet uses words differently than typical sentences.  He does not capitalize, and does not even put spaces between the words (“travelled,gladly”).  By doing this, he reinforces the tone and message of his poem, about the facts of life.

Poetry speaks directly to emotions.  It seeks to eliminate as many barriers as possible between the poem and the reader.  There is a little more distance in prose.  Prose consists of novels and drama.  It is basically writing like human speech.

The difference between drama and novels is the purpose and the structure.  Drama is written to be performed.  It can consist of prose or be more like poetry, such as Shakespeare.  It is composed of stage directions, speaker tags, and lines.  Here is an example from the play The Diary of Anne Frank.

Miep. Are you all right, Mr. Frank? 

Mr. Frank (quickly controlling himself ). Yes, Miep, yes. 

Miep. Everyone in the office has gone home. . . . It’s after six. (Then, pleading) Don’t stay up here, Mr. Frank. What’s the use of torturing yourself like this?  (Act 1, Scene 1)

A play is meant to be performed, and not just read.  The stage directions tell the actors what to do, but also describe the action of the play and how the lines will be delivered.

A novel, on the other hand, is a story written in paragraphs.  It includes the narration, as well as dialogue.  Here is an example from To Kill a Mockingbird.

"Teach me?" I said in surprise. "He hasn't taught me anything, Miss Caroline. Atticus ain't got time to teach me anything," I added, when Miss Caroline smiled and shook her head. "Why, he's so tired at night he just sits in the livingroom and reads." (ch 2)

This excerpt shows dialogue, action, and how the character felt.  By using this genre, we can tell a fuller story than poetry or drama.  There is more detail, and characters and events are more fleshed-out.  This genre is more character driven, where drama is more plot driven and characterization is accomplished through action.