How to highlight the importance of past positions in CV? When addressing the past positions in a resume, although titles somewhat describes the role, they cannot clarify the importance of positions.

For example, listing a past position of department chair indicates administrative duties at department level, but it depends on the department. Definitely, chairing a small department with a few faculty members and annual enrollment of 30 undergraduate students is different from a well-funded department with tens of senior faculty members and several PhD programs. However, if a reader does not know that specific department, the term department chair is the same.

This is even more serious when it comes to differences in terminology. In a university, a faculty can be equal to a department, and somewhere else a faculty can be in the size of a university hosting several large departments. Even terms of mid-level administrative positions in academia do not always have the same meaning: e.g., dean, director, chair, head.

How do you fairly clarify the importance of the job you had?

It is possible to add a description, but as it is not very common, it may cause an impression of overestimation.
If a title or position is unclear, or an institution is possibly not well known, just explain it in a few words:


  
  Director of Supersonic Operations department (15 researchers) at Small U.
  Time-management officer, Funny Inc. (in charge of scheduling company-wide meetings)
  Information officer, U. of North Virginia (CTO-like position, managing computing resources for 10,000+ students and staff)
  


Be as concise as possible, but give the reader some idea of the scope of your activities. And if the position is clear or well-known, just don't add any details.