"This was their finest hour" was a speech delivered by former British Prime Minister Winston Churchill on June 18th, 1940. This was the third of 3 speeches at the time France was dealing with the German invasion.
Churchill appeals to "Pathos", which is a rhetoric technique that aims to reach the sentiments of the people who one is trying to reach with his or her message. Words like "Blood, toil, tears, and sweat" were used during his speech in an effort to depict the current situation of the forces who were fighting against the Germans. He concluded his message by indicating that "his professional advisers had strongly suggested him to proceed with the war and that there are good and reasonable hopes of a final victory".