Make Unique makes a map instance into a unique copy. It also makes an instanced sub-material into a unique, standalone sub-material. It gives the sub-material a new material name. (A sub-material is a material within a Multi/Sub-Object material.)
Using Make Unique prevents changes to the top-level material instance from affecting the sub-material instance within the Multi/Sub-Object material.
You can also use Make Unique at the map level, when a map is instanced to different components of the same material.
Note: If you drag an instanced map to a Material Editor sample slot, the Make Unique button will not be available, because it is not clear from the context what it would be unique relative to. Instead, you need to bring one of the parent maps or materials into the Material Editor, browse down into the map, and then make the map unique relative to that parent.