A product owner distils the needs of the users/customers into a long term and short term roadmap usually called a vision or strategy. Also, s/he works daily with engineers to develop, prioritize, and groom a backlog. The highest priority backlog items, also known as user stories, are taken up and tested by the engineers. When the user story is considered complete, it is demonstrated back to the product owner who accepts or requests changes to the original user story.
This process happens in a consistent cadence, usually, 2 - 3 weeks, called an iteration or sprint.
The purpose of this iterative process is to produce a continuously improving product for the users/customers.