This film is often discussed in US history textbooks as a commentary on the conformist society of its time.
You can see this in the main plot of the film. When the people are replaced by the beings from the pods, the new beings are completely emotionless. It has been argued that these are the people of the '50s -- they do not have an emotional life, they are just drones. In addition, the pod people start to propagate themselves. They are trying to create more pod people so that soon everyone will be the same -- emotionless automatons that are not really human anymore.
Because of this, the movie is often seen as a warning that Americans were coming to be like this -- all the same, all without souls.