What does a Product Manager Do?

"What does a Product Manager Do?"

My own understanding is that a Product Manager's job includes:
0) Product's Core Value and Competition
1) Product Architecture
2) Product Life Cycle or Time Table (and management)
3) Communication
4) Also, in my position, I need to code all algorithms and data I designed

Then, I searched the website on the topic, and get something:
From: http://www.smashingmagazine.com/2014/09/17/why-companies-need-full-time-product-managers/

With that as the backdrop, my definition of the role of a product manager would be to achieve business success by meeting user needs through the continual planning and execution of digital product solutions.

...

Marty Cagan has a great list of common tasks that product managers are responsible for in his ebook Behind Every Great Product (PDF). The tasks include:

1. identifying and assessing the validity and feasibility of product opportunities,
2. making sure the right product is delivered at the right time,
3. developing a product strategy and road map for development,
4. leading the team in executing the product’s road map,
5. evangelizing the product internally to the executive team and colleagues,
6. representing customers through the product development process.