The definition of a sub-object element depends on the modifier. For example it may be a modifier's gizmo or part of its gizmo. Consider when an FFD modifier is in vertex sub-selection mode, the sub-object elements that are being hit tested are the control points of the lattice. Edit modifiers usually hit test components of the object in the pipeline such as vertices or faces.
When a modifier's HitTest() method is called, it traverses the sub-elements of the current sub-object selection level and checks each one to see if it has been hit. If so, it registers a hit record with the active viewport. A hit record contains the following information:
When Modifier::HitTest() is called by 3ds Max on an edit modifier, the edit modifier needs to hit test elements of the object that is flowing through the pipeline. This presents a problem since a modifier usually only has a pointer to this object when its ModifyObject() method is called. In order to be able to hit test the object, a modifier must keep the object cached. Caching the object the modifier is modifying is generally useful as well. For example, the Edit Mesh modifier keeps a cache of the mesh it is editing. When the Edit Mesh modifier is evaluated, if it has a cache it can simply return the cache. This way, as the user applies incremental edits to the mesh, all of the previous edits don't need to be reapplied. Instead, when an edit is made it is applied to the cache and stored away in some form in case the modifier needs to be reapplied.
Modifiers can be instanced, so storing an instance-specific cache in the modifier might not be the best idea. It is the ModContext specifically in the ModContext::localData field, where instance-specific modifier data belongs. This is where edit modifiers can put a cache of the object that it modifies.
Note: typically this cache is only needed while the object is being edited. A hit test will never be called on a modifier unless it is being edited. In terms of evaluation, the pipeline already places caches where appropriate so there is normally no need for the modifier to maintain a cache.