Just a brief
addendum to the
formal explanations above:
The villanelle, like the sestina, is really a metapoetic form, which is a fancy way of saying that it's so highly stylized that it ends up pointing out the artifice in all poetry.
What this really translates to is a form dearly beloved of conservative poetry MFAs, since it allows the author to simultaneously play off a tradition and mock it. In this way the villanelle form is tiringly postmodern. Writing this type of poetry is actually fairly easy, since the only real prerequisites for carving out a villanelle are the ability to rhyme and a knack for iambic pentameter. One does not need to be daring or even original when writing in such an elevated form - the simple fact that you've written a villanelle is enough to impress a good many readers and, of course, the occasional poetry journal editor. Sure, you have to make sure it's not painful to read, but other than that you've got it made. This is intended as a dig at the poetry establishment, not at any particular writer.
Most people, including poetry students, really get by on three villanelles: "Do Not Go Gentle Into That Good Night" by Dylan Thomas, "One Art" by Elizabeth Bishop, and "The Waking" by Theodore Roethke. Obsessed fans of Sylvia Plath would really like to add "Mad Girl's Love Song" to that list, but it ain't happening since it's aggressively end-stopped, and the overuse of parentheses to get around what would otherwise be a cumbersome treatment of the repeated lines is widely considered cheating.