Chaplin's Dislike of Hitler
The central theme of the movie is Chaplin's own dislike for Adolf Hitler and his regime. This also extends to dictatorships in general; at the time, the rise of Fascism in Europe was deeply troubling, and there seemed to be many nations with a Fascist dictator at their helm. By lampooning Hitler, Chaplin drew attention to his many personality disorders, his despotism, his innate hatred for anyone not fitting his Aryan picture of the ideal human, and also the way in which he was not smart enough to develop his own policies and therefore relied on other, more dangerous minds to do this. He also draws attention to the fact that the German people were either mostly in agreement with Hitler, or extremely gullible in the way they fell hook, line and sinker for his rhetoric.
The Holocaust
The Barber is already living in the ghetto, which is where the Jewish citizens of those countries under Hynkel's control had been sent, forced to leave their own homes and now living in far worse conditions. The Barber is then arrested and sent to a concentration camp. This is exactly what happened in German under Hitler's regime, and the way in which the Holocaust was able to gather steam and momentum is shown satirically by Chaplin in the movie.