In an agile world the development process (sketched above) is less important compared to results. So as an overlay on the five key tasks of a product owner the next picture shows the key artifacts that are created and maintained over time. We use a color code for the artifacts: green indicates artifacts that are normally considered to be requirements artifacts. Red is for artifacts normally considered to be management artifacts. Since a product owner is a combination of manager and requirements engineer (or business analyst) he or she has to deal with all green and red artifacts.
The development team(s) will iteratively create product increments based on the priorities defined by the product owner. Artifacts of the development team are shown in blue. At the end of each iteration the product owner has to check and accept (or reject) this product increment.
Note that the product owner has more to do than just maintain the backlog of functional requirements!
Key Artifacts for Product Owners