The list of objectives shows the goals that were used in building rules in this project. Each objective is created in the rule writing process and should describe the reason why a particular rule or set of rules was added. They can also be used to provide some other note that you may want to attach to that rule.
Objectives may be organised in a hierarchy, with the more general objectives at the top, and each of these being broken down into more specific objectives shown underneath.
When you select an objective using the explorer, the list of rules where that objective has been used are shown in the right hand pane.