This option determines whether the modifiers name of all objects are shown in the object list. Together with the objects names you can configure LEX to show any object attributes to be shown directly in the list as additional columns:
There are five important basic information for each object, which can be chosen directly to be shown as a list column or not. The Modifiers Name is one of them: This is the distinguished name of the account which accessed and modified the regarding object. This is the standard attribute modifiersName which is defined in the LDAP v3 RFC 2251 and which is supported by a lot of directory servers (unfortunately, Active Directory doesn't support it).
You could configure the Modifiers Name option also by opening the context menu of the object list column header - just right-click on the column header: