To control what nodes you prefer displayed in the navigation pane, click one or more nodes in the selection list. Click a node to display it in the navigation pane; no check in the check box removes those nodes from the navigation pane.
When you choose to display all partitions, this refers to all the partitions defined to your server in the Work pane.
When you choose to display all objects, this refers to all objects (Servers, Partitions, Frames) managed by this HMC in the Work pane.