A product manager does many things. A product manager is like a CEO with all responsibilities except any of the authority.
Here's a list of skills that tech companies look for in product managers:
Technical Skills - Coding level knowledge. Some companies prefer software development as a prerequisite for product managers, Some don't. A good technical understanding will never hurt.
People Skills - Build communication and trust from your development team.
Data-driven - SQL, Excel, etc.
Strategic Thinking - Product strategy. Game theory.
Good Design-sense - Markup/wireframe.
Experimentation Mindset - A/B testing.
This post is a case study of my latest project. The resultant product is a pair of websites designed for new Bitcoin (a crypto-currency) users. I laid the ground work of inbound marketing in September (3 months ago) along with market research and planning. It is not until recently I started the design and development in anticipation of a full rollout planned in the coming year 2014. The websites, bitcoin-tw and bitcoin-en, are partially live and open to the public as of this writing.
The role of product manager is viewed as a business function to maximize ROI in the product, maximize market share, revenue, etc. for business success. Product managers work with engineering and across the business to make sure the software product is well built and defined.
I personal think an entrepreneur should be a product manager in his/her soul.
What does a product manager do?