As per the Scrum guide “A Scrum Product Owner is responsible for MAXIMIZING the value of the product resulting from the work of the Development Team." To meet this statement a product owner has to participate in several activities, talk to the stakeholders, do research work, etc. The product owner has to attend a meeting with the team which is PLANNING or pre-planning or any of the scrum ceremonies. To make sure the product owner ADDING value to these meetings with his presence, he/she has to spend a lot of time talking to various stakeholders and understand their problems and area of work. 

They also capture the metrics RELATED to the product backlog to understand the state and USE for reporting. They speak with UX designers or the Architect to identify how we can improve the system to remove the customer pain area. During the course of the day, the teams contact the product owner to clarify the doubts on requirements. Apart from this, there will be status update meetings for each project. Along with all this, the product owner has to keep the backlog healthy and prioritized.