Offices held or honors refers to positions you have in the company or career field (offices held) and any awards you have received (honors).
An example of a doctor's "offices held and honors":
-Specialty Fellow, American Academy of Pediatrics
-Member, Program Advisory Board, American Academy of Ophthalmology
-Honor Award, American Academy of Ophthalmology
-Professor, Medical College of Wisconsin
The format for this is "position, place/organization" or "award, place/organization"
hope this helps! :)