The Dependents Pane allows you to trace the dependencies for the currently selected package. The the dependencies are the list of other packages that depend on this package being loaded first before they can be successfully loaded themselves. Dependencies are effectively the opposite of the package prerequisites.
In the top half of the Dependents Pane is a tree view that shows the current package at the root and the dependent packages at levels below this. Selecting the dependent packages in this list will display the actual prerequisites in the list in the lower half of the pane. By looking in this list you can see exactly why one package depends on another.
It is important to realize that the Dolphin package system will not allow you to save out a package which has an implied circularity in the prerequisites/dependencies. If you are warned that a particular package cannot be saved then you will need to trace through the dependencies to find where the circularity occurs and rectify it. See Tracing Circularities in Package Dependencies for more details.