When working with Scrum, the product owner is typically a project's key stakeholder. It is important that this person has a vision of what they wish to build and that he or she is able to convey that vision to the scrum team. This is key to successfully beginning any agile software development project. The Agile PO does this through in part through the product backlog, which is a prioritized features list for the product.
The product owner is commonly a lead user of the system or someone from marketing, product management, or anyone with a solid understanding of users, the market place, the competition, and of future trends for the domain or type of system being developed. This of course varies tremendously based on whether the team is developing commercial software, software for internal use, hardware, or some other type of product. The key is the person in this role needs to have a vision for what is to be built.
Although the agile PO prioritizes the product backlog, during the sprint planning meeting the team selects the amount of work they believe they can do during each sprint and how many sprints will be required. The product owner does not get to say, "We have four sprints left, therefore you must do one-fourth of the product backlog this sprint." The product owner's job is to motivate the team with a clear, elevating goal. Team members know best what they are capable of and so they select which user stories from the top of the product backlog they can commit to delivering during any sprint.
In return for the scrum team's commitment to completing the selected user stories from the top of the product backlog, the product owner makes a reciprocal commitment to not throw new requirements at the team during the sprint. Requirements are allowed to change (and change is encouraged) but only outside the sprint. Once the team starts on a sprint it remains maniacally focused on the goal of that sprint.