You can find more details about the Annotation Monitor and the ANNOMONITOR variable in the Help files at the links highlighted.
A new feature called the Annotation Monitor was introduced in AutoCAD 2013-based products that is shared with AutoCAD Plant 3D 2013 that shows dimensions and leaders that have lost their associativity.
When the geometry associated with the dimensions is moved or changed, the dimension values will update when associativity is enabled.