Ariba documented this well in the API PDF. See Chapter 7 "Business Objects" that then describes Clusterroots and BaseObjects.
Example Clusterroot are Suppliers. The data can be reused for any approvables. A BaseObject has self contained data that is only relevant within the approvable you're working with. So, use an example of Requisition, off the line item the Clusterroot Supplier will be linked there, but you could also have free text field of type longstring that is a BaseObject. It has no meaning outside of the context of the approvable and as a BaseObject it's not queryable as a class from Inspector, whereas a Clusterroot can be looked up by itself from Inspector (Query Supplier object rather than querying suppliers from a Requisition).