If you're playing as a dedicated warmonger and the Amenities penalty is taking a toll on your cities, you can use Propaganda to help lift your people's spirits. It's a decent go-to policy if you have nothing else to put in one of your government's Military slots. Note that it replaces Retainers, so you'll no longer be able to receive an extra Amenity in garrisoned cities once Propaganda becomes available.
Social psychologists have studied propaganda, and while it cannot change beliefs or convictions, it can reinforce these or cause doubt about other ones. Propaganda shares some techniques with two other mass-media phenomenon, advertising and public relations … and truly it is tough at times to distinguish between the three. Although there have been instances of propaganda ever since the printing press was invented, the coming of film and broadcast brought propaganda to the forefront during the first two world wars, and the subsequent Cold War. So virulent did the propaganda become that the United Nations added Article 20 to the International Covenant on Civil and Political Rights in 1966 which prohibited any propaganda for war or any advocacy that could lead to violence.