Research, analyze, define product features and you create metrics to measure the impact of your product to the company
Be the primary driver of your product's planning and execution
Write the specs of new features and enhancements
Come up with product road map and rally other people to join your cause to realize your product vision. You are expected to be able to prototype your vision to convince others if necessary.
Work with engineers, designers, ops, sales, legal and even external partners to make things happen