Tip: switching between different view modes(priority/hierarchy etc) is done by clicking the tab next to Backlog item. The tab title will always display the currently selected view mode.
The main goal of this view is to prioritize items on a higher level for the project.
The normal workflow for a backlog item is to enter it (or commit it from the product backlog) into Items in a hierarchy and then prioritize it among all other items in "Items prioritized" (independent of the hierarchy).
You can set priority in "Items prioritized" by either dragging items up or down, or by selecting from "Product backlog priority" column:
You can set the priority in "Priority view" by selecting from "Product backlog priority" column:
You can set the priority in "Board view" by selecting "Product backlog priority" as your board mode:
You can select a custom drop list column as your Product backlog priority by going in to "Customize project" and then "Priority":