Product manager, IMHO, is an owner of a product and therefore responsible for the success of the product. That means the role and responsibility of a product manager touch on many aspects of product development and delivery. I have been a product manager at a social gaming and a web company, so my answers have to do more with such space.

- Own analytics. Don't trust qualitative stuff, but trust quantitative stuff. Track important metrics and monitor performance. One of the metrics should be revenue generation.

- Do many experiments on subset or all users. This is our way of finding out what customers want. First is intuition, but verify it with experiments.

- Own and prioritize specs and stories (in agile dev sense). This is where the cross with business part comes in and kinda obvious. Spec/story priorities should align with business objectives.

- User acquisition and retention. This part touches on marketing part. How to get new users? How to retain users? Social media? Email campaigns? Contests? Sweepstakes? Partnership?

- Etc., etc., etc.

But, ultimately, PM is responsible for success of product(s) s/he manages, and thus do whatever is necessary to make it happen.