Churchill was on an oratorical roll in May and June of 1940. In the course of a few months, he gave four speeches that people like you study all the time. The June 18 speech was like the earlier ones: it laid out the problem (this time it was France that had just surrendered) and offered encouragement that the threat would be met with everything Britain had. With France gone, Churchill knew that Britain would be next on Hitler's hit list. The stakes were high:

Hitler knows that he will have to break us in this Island or lose the war. If we can stand up to him, all Europe may be free and the life of the world may move forward into broad, sunlit uplands. But if we fail, then the whole world, including the United States, including all that we have known and cared for, will sink into the abyss of a new Dark Age made more sinister, and perhaps more protracted, by the lights of perverted science.

Let us therefore brace ourselves to our duties, and so bear ourselves that, if the British Empire and its Commonwealth last for a thousand years, men will still say, "This was their finest hour." (Source)

The British Empire didn't do so well, but facing down Nazi Germany was definitely a pretty fine hour.