A product manager manages one or more tangible products while considering the competitive analysis, market analysis for a business fit.
Here is the definition from Wiki -
A product manager investigates, selects, and develops products for an organization, performing the activities of product management. A product manager considers numerous factors such as intended demographic, the products offered by the competition, and how well the product fits with the company's business model. Generally, a product manager manages one or more tangible products. However, the term may be used to describe a person who manages intangible products, such as music, information, and services.
In a Scrum environment, a Product Manager is also referred to as the Product Owner, and usually has the main role of representing the product to the customer. Some of the responsibilities of the Product Owner include marketing of the product and analysis of the competition.