When you clone an object, you can make it an instance or a reference. If you make changes to an instanced object the changes are also reflected in the other instances in your scene. And when you change a referenced object, the changes affect objects that refer to it. Making objects unique lets you adjust or change those objects independently without affecting any other objects in the scene.
Similarly, when you apply a modifier to multiple objects simultaneously, the modifiers are instances of each other and changes to one affect all of them. And as with objects, making a modifier unique lets you change it without affecting the former instances.
Example: Use Make Unique with an instanced modifier:
When the Clone Options dialog opens, make sure Object is set to Copy.
You now have four cylinders with a single instance of a Bend modifier applied to them.
This lets you return to the current state of the scene at any time without using Undo.
The modifier stack shows the modifier but not the geometry, because the latter isn’t instanced between the two objects.
The Make Unique dialog opens, asking whether you want to make the selected items unique with respect to each other.
At this point, the two selected cylinders each have unique Bend modifiers, while the remaining two cylinders share the original, instanced Bend. You can see this by selecting each cylinder and changing the Bend Angle setting. Changing one of the unique modifiers doesn’t affect any other object, while changing one of the instanced modifiers changes the other object with an instance of the modifier.
The two selected cylinders now share an instance of a Bend modifier, but it's a different instance than that shared by the other two cylinders. Again, you can see this by selecting each of the cylinders and changing the Bend Angle spinner. You can also turn on Show Dependencies in the Views menu to see the relationship between the four cylinders and the Bend modifier.
Example: Use Make Unique with an instanced object/modifier combination:
Both cylinders bend.
When you change the Bend Angle setting or cylinder base parameters for one of the objects, the other doesn't change.