The Stakeholders are the people who are invested in the outcome of your project. It is up to the Product Owner to understand the outcome required by the Stakeholders, and to communicate that need to the Delivery Team.
Their participation in the project is essential for success. For example, when your team is performing the Sprint Review meetings, the demonstration of the project is for the stakeholders, and their feedback is captured and added to the backlog. Different groups of stakeholders can share their feedback in different ways. Usually participants of the business side of the project are involved in the development process, while input from customers/users can be provided e.g. by web analytic tools.