I'll give it a shot. Having been an NCO for many years, I'll give you my take. An NCO is an enlisted person who has been delegated leadership and command authority by a commissioned officer. We are the mid-level managenment of the military. We are often referred to as the "backbone" of the service.
We have multiple responsibilities. We serve as advisors to the officer corps and supervisors and advocates of lower ranking enlisted personnel.
The tradition of the NCO is often traced back to the Centurion of the Roman Army. There are junior and senior NCOs in the Army, and petty officers in the Navy.
NCOs are trained through a series of advanced schools (NCO academies). You can see the NCO development ribbon for each level of training on an NCO's uniform.
As far as what a commission is, it is a government document that confers the rank of an officer on the recipient. Hence, no such document equals a Non Commissioned Officer.
I hope that helps a bit. But if you have further questions, just ask.
I hate newspapermen. They come into camp and pick up their camp rumors and print them as facts. I regard them as spies, which in truth, they are.
Gen. W.T. Sherman