Articulate the problem
Understand the customer (through research etc)
Determine the KPIs/Goals for the product/problem area
Collaborate with all stakeholders (execs, eng, design, customers, partners, product marketing etc) to determine the priorities
Articulate a compelling vision and drive alignment across all stakeholders towards that vision
Develop and evangelize a roadmap to all key stakeholders
Drive the design and feature specs for each iteration
Work with the craftspeople (designers, engineers, data scientists etc) to turn concept into reality through a regular cadence of checkins, reviews, and other project management techniques
Work with Product Marketing/Sales/BizDev to announce and drive adoption
Measure the results against the KPIs/Goals
Rinse and repeat
See responsibilities of a Group Product Manager/VP of Product/CPO Here