The 'Layerize' tool allows the user to move EVERYTHING that is selected to a particular layer. This includes groups, components and anything inside the groups or components.
Google SketchUp's default behavior when changing an object's layer is to move only the top-level item to the new layer. If the user selects a group, then changes it's layer, the group will exist on the new layer, but the entities within the group will remain on their current layer.
The Layerize tool will go inside the group and move all of those entities to the new layer as well. This functionality eases the organization of a model for 3D printing.