A product manager is a person responsible for coming up with product offerings and shipping them to the customers with the help of various teams in the organization.
It is his responsibility to maximize profits and optimize the product as per user needs.
As a product manager you have to make sure all teams work together to achieve a shared goal but you won’t have authority over all the teams.
It is the interpersonal skills and vision of an individual that can help them succeed as a product manager.
Read https://www.feedough.com/product-manager/ article for better understanding of what a product manager is.