During the Cold War, the "Free World" consisted of all the states aligned with the United States of America:

As you can see, the level of political and economic freedom in many of these countries was rather lacking, so the name wasn't exactly deserved, especially considering that if you were looking for a free, as in beer world, you'd have to go to the Communist bloc. Back in the day, the view was that dictatorships were at least workable, in contrast to totalitarian states which were basically a lost cause. This logic led to the development of the Kirkpatrick Doctrine.

After the collapse of the USSR, the Free World fell into rhetorical oblivion of sorts. Although the President of the United States of America continued to be referred to as "leader of the free world," the lack of a viable non-free world to compare it to made it seem antiquated, and more people began talking about "the West" and "our allies."