I have come across this phrase a number of times since and in a variety of forms. Quite a few people claim authorship, others attribute it to well known books about the habits of successful people and some point to its roots in religious texts (if he is reading, Ben might be able to clarify for us here!).
Rather than its origins, its relevance in a career context is all in its meaning and practical application. Seeking to understand forces an individual to test their ambitions externally rather than basing them purely on internal assumptions.
Seeking to understand is also useful for the role it can play in identifying opportunities for career development and personal success. If you can understand their priorities and what an individual or a business needs, you are creating a broader context for your skills and experiences to be seen as relevant.
While it can never be the only component of a successful career plan or leadership career, seeking to understand is a simple and effective means of keeping your activity meaningful to you and those around you. The successful career of the interviewee who introduced me to the subject is a excellent example of that.