Clarify the statement: "the business of business is business."
It strikes me that you may also be referring to the quote from President Calvin Coolidge in the 1920s:
"After all, the chief business of the American people is business."
Coolidge was a very pro-business President and a advocate for little if any regulation on business activities.
In the modern sense, that quote has been used again and again to describe the modern supereconomy of the United States as being based on capitalism, and on small businesses in particular. The suggestion that, today as well as in Coolidge's time, business should be free from constraint so as to promote economic growth and job creation is a very common one, especially in time of recession.
To me, this statement means that the only goal of a firm should be to make money. Firms are created in order to do business and to make money while doing it. Any other goals are not really appropriate for businesses because their goal is to make profit.
This sort of a statement is often made in response to the idea that firms should be more concerned with social goods. In other words, you will hear that firms should be more "green" or that they should try to do more to help the poor or other things like that. The statement you have given us is saying that such things are not the concern of firms -- individuals or governments may care about such things, but the goal of a firm is to make money.