For the reviewers (the "Vine Voices"), it looks like this: on a regular basis, you can choose a product to review (based on your past reviews, purchasing history etc., maybe - they don't disclose how that works), and Amazon sends the product to you. Within one month, you have to post a review.
You can post whatever review you want; to become a Vine Voice, you need a reasonably high reviewer ranking (mostly based on "helpful" votes: [1]). The reviews are labelled as written by a Vine Voice.
As a side note, I know a Vine Voice, and they get emails from companies offering to reimburse them for a product in exchange for a five star reviews every few days.
[0]: https://www.amazon.com/gp/vine/help
[1]: https://www.amazon.com/review/guidelines/top-reviewers.html/