Historically, "liberal" has not always referred to a "left-of-center" world view, just as it has not always been in opposition to "conservative." In basic terms, to be "liberal" was to be open and accepting, tolerant, and with a mindset towards freedom and limited government. Wikipedia defines it as follows:
Classical liberalism is a philosophy committed to the ideal of limited government and liberty of individuals including freedom of religion, speech, press, assembly, and free markets.
This seems strange considering the connotations of "liberalism" today -- by the way, it is important to note that these terms mean different things in Europe and elsewhere than they do in the United States. The above definition is more aptly represented in the U.S. by the libertarian movement, insofar as it can be defined.
In any case, liberalism in 1939 was still finding its new footing. Franklin D. Roosevelt, in his chairing of the fledgling Progressive movement, changed liberalism from a general focus on freedom to a general focus on government action to support the national interest. This flew in the face of Classical Liberalism, and so the ideology split off into Libertarianism and Modern Liberalism. The term "progressive" stayed relatively low-key until the mid-nineties, when politicians started using it to differentiate themselves from "the other guys."
FDR, then, used his administration to plant the roots of Modern Liberalism as we know it today, focusing on the government as a major part of a citizen's life. Liberalism in 1939 had a focus on the general welfare (stemming from the continuing Great Depression), equality in the workplace and society, full legalization of labor unions (the source of much economic dispute until then), price controls and minimum wage standards, and the continuing of private company control (Roosevelt was on record in opposition to socialism, and during the New Deal only one program specifically came directly under government control).