In Churchill's time there was a doggerel limerick that went like this:
There once was a lady from Niger, Who smiled as she rode on a tiger. --They returned from the ride --With the lady inside, And the smile on the face of the tiger.
Churchill intends to illustrate the precarious position of a dictator as he brutally rules a nation that basically outnumbers him. The tiger getting hungry is the nation the dictator rides, with the hunger symbolizing a growing appetite of the nation for revolt against the dictator.