The Select Other tool appears when you hover cursor over an object in an Inventor Publisher document. Hovering your cursor over the Select Other tool display a drop-down menu including two options, By Depth and Parents.
Select by Depth
When you work with a complex model, it is not very easy to select the components which are blocked by the others. The By Depth sub-menu speeds the selection process by making your selection directly from the menu.
The By Depth sub-menu is also applied to selecting edges and faces when you create three quarter section view and add some annotations.
Select Parents
The Parents sub-menu lists all the sub-assemblies and assemblies containing the selected component.
Select Other Tool