I'll stab at it.
Spock wrote:The needs of the many outweigh the needs of the few
Vulcans were logical and liberals. The common good is the concept of serving the needs of the many over the needs of the few. Which is, for the most part, a logical statement in the philosophy of ethics. I believe it's origins of the statement can be traced back to Emmanual Kant.
What makes the term so elusive to define is the fact that it covers an eclectic mix of subjects and is itself subject to subjectivism. Exactly what is good for everyone and what is not? The answer is mostly subjective.
For instance, certain infrastructures such as electrical power generation and distribution and heating gas and oil production/distribution should be regulated so that the heating needs of the many are served over the profiteering needs of the few. Everyone should have heat - that is a 'common good'. But to ensure the common good, the few must endure limited profits - or higher taxation.
subisdies and regulations can also be for the 'common good'. Everyone deserves to eat, to drink and to breathe. Ensuring those three things is for 'the common good'. But to ensure the common good requires subisdies for production and distribution, and regulations to ensure at least a minimum acceptable quality.
So the common good is literally the philosophy of placing the needs of the many over the needs of the few.
But what about things like narcotics, abortion, or health care? Should everyone have free and easy access to any or all of them 'for the common good'? Some would say yes, and others would say no. Thus, the term could become a sort of litmus test for liberalism.
However, sometimes attempts to promote the 'common good' have unintended consequences. Some attempts to promote the 'common good' might actually have the opposite effect. For instance, overly restrictive regulations upon economic competition for the 'common good' can have an unintended consequence of reducing the economic welfare of the whole of society. But overly permissive regulations can also harm 'the common good' with fraud, corruption, monopolies, and other economic problems detrimental to society as was demonstrated in the American 1920s and 30s.
Sometimes we go overboard both ways.
Or I could be way out in left field somewhere....