Does the Product Owner own the product?

This is a misconception among people that are new to Agile Scrum.

The gathering of requirements for an agile project is the responsibility of the Product Owner. These requirements are then written as user stories from the users perspective by a Business Analyst or they are written as features or epics which are further broken down (into smaller chunks to fit into a sprint) for the developers to work on them.

The Product Owner is a member of the Scrum team, an internal stakeholder who acts as a liaison between the Scrum team and the other stakeholders (this includes the customers). By virtue of this, he understands the product vision and has first-hand knowledge of the customer's expectation (product goal).

The Product Owner owns the product backlog where the gathered requirements are stored and refined for the Agile project iterations.