When I classify an object as primarily being a structurer, I think first and foremost about what relationships it should maintain between other objects and how it should do so. Structurers are common stereotypes in business applications where relationships between objects can be quite complex. Some objects exist to manage these connections. Let's take a simplistic real world example of a file cabinet containing folders that hold documents. In this example, a file cabinet doesn't do much, it holds folders that may be tabbed and labeled.
Folders simply hold their contents.
It is the documents that are of interest. In an object design, I add more or less behavior to objects to meet business requirements and to suit my personal design tastes. I can design File Cabinets to do more than organize their contents. A File Cabinet could know when any folder was last referenced, or how much room is left in the cabinet. Information Holders keep facts that other objects can ask about.