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 Analytics - Use SQL, Excel, etc. to make data-driven decisions. Put product investments in the areas that will produce the best return on investment.
Strategic Thinking - Product go-to-market strategy. Game theory.
Good Design-sense - Markup/wireframe.
Experimentation Mindset - A/B testing.