Question

What did winston churchill mean by this?

Answer 1

He meant that if they failed then everything that the world has worked so hard for, to advance and become "smarter" than we once were would all be for nothing. We would enter a new Dark Age. The Dark Ages were an extraordinarily difficult period in the story of humanity. It is estimated that 100 million people died at the hands of war, poverty, and plague. But during this time new ideas and ideals were born and much of the groundwork was laid for the world we know today.

Answer 2

It means that if the Armed Forces and the British people (at great sacrifice) of Great Britain fail, then the whole world will change for the worse and a new age full of unknown horrors will be thrown into a deep dark inescapable  pit. Even the United States, with all its, power, will not escape this fate.

The Dark Ages were a particularly black period in Western Civilization's history. Education was frowned upon and those working in agriculture (most people) growing the food we need, were no better than slaves to the Church and to the Nobility.