Poetry is a form of non-prose writing that is meant to create an emotional response through sound.  Sound in poetry is created through repetition, rhyme, and/or rhythm.  Finally, meaning is created in poetry through the use of symbols, images, and/or figures of speech.

To be honest, I'm not sure what your class has gone over as the three major sub-genres of poetry (as there are more than three), but my guess would be this:

1. lyric - most common poetry; usually written in verse; ex: Robert Frost, William Wordsworth
2. ballad - long story (like a folk tale) often about love, with a repeated refrain; often set to music; ex: The Mermaid (unknown), The Ballad of Persse O'Reilly (James Joyce)
3. epic - long narrative poems that are usually about a hero on a journey; ex: the Iliad and the Odyssey