In the context of Agile and Scrum, the term product refers to what the Scrum Team is developing. This could be a software application, a service or a physical product.
It is important that the product delivers value to the end-user or customer. Moreover, a product evolves as the needs of the users change. With Scrum you are better positioned to respond to these needs and continue to deliver a usable product.
Furthermore, in Scrum the product is often considered to be the work that the Scrum Team produces during the Sprint. Each Sprint delivers an incremental addition to the product. Thereby gradually improving it.
In Scrum, there is also the role of the Product Owner. He/she is responsible for maximizing the value of the product. How this is achieved can vary greatly between organizations, Scrum Teams and individuals.