Summary : The way how to perform the Product Owner duty can be divided into two parts: Managing the Product Backlog; and Collaborate with the Team.

What are the Product Owner role and his responsibilities?

Scrum Guide explanation of the Product Owner role is "responsible for maximizing the value of the product resulting from work of the Development Team'‘. The way how to perform his duty can be divided into two parts:

Managing the Product Backlog; and
Collaborate with the Team.

Manage the Product Backlog

The Product Backlog is a list of requirements needed for the product. The Product Backlog items are prioritized by the Product Owner, and anyone could add items to it. The scope of the Product Backlog management include

Clearly describe Product Backlog items;
Decide the priority of Product Backlog items;
Optimize the quality of the work done by the Development Team;
Ensure the transparency of the Product Backlog and the Development Team understand it as required

Although anyone of the Scrum team can add items to the Product Backlog, only the Product Owner can decide what will be included in it for the Development team to achieve. The Product Backlog refinement is introduced to review and revise the items.

Collaborate with the Team

The Product Owner is accountable for the work delivered by the Team. So he is responsible for defining the vision for the Team to visualize the expectation by a product roadmap. The Product Owner also acts as a liaison between the Team and the stakeholders. He ensures the Team understand the requirements and interact and collaborate with them on delivering the quality. He is equally important in communicating with the stakeholders about the goals.

The way that the Product Owner work with the Team also includes

Monitor the progress of team backlog item in each Sprint;
Participate in Scrum meetings, including Sprint Planning, Sprint Review and Sprint Retrospective;
Inspect and adapt to impediments the Team encounter

Challenges for the Product Owner

The Product Owner is a person, not a committee, so it is not easy for just one person to make decisions for the whole team. The product is facing challenges from both the inside and the outside of the Team. Common pitfalls might be

The missing product roadmap
Priority change in the progress of doing a Sprint
Acceptance criteria overly set
Too much time spent on support rather than the Product Backlog.

The skills required for being a competent PO is to be knowledgeable about the product, extremely communicative, and agile. He also has to be a great storyteller and an issue solver who always has the final say to things. If you have any ideas, feel free to comment below.