The role of that checkbox(as of any checkboxes attached to various parameters you can set for an object in the Naming tab) is related to the numbering, and tell AS if to ignore or not that parameter when its doing the identical part detection.
For example, you have two identical beams. You assigned the model role "Beam" to one, and "Rafter" to the other one.
If the checkbox is not checked, then when you do the numbering the two beams will get the same Sp mark. The two objects will still have a different model object, which will influence various operations that require a model role filter, but from the numbering point of view , the two objects will be the same (so for example you'll get one single part drawing from it, with the quanitity 2x)
If the checkbox is checked, the the two beams will get different part marks. Even if they are identical from the geometric point of view, due to this different model role combined with the checkbox, AS will treat them as different objects.