Essentially, it was a series of compromises between classicists and positivists. It stressed individual accountability and individualization of punishment. The positivist school is best seen as a reaction to the armchair philosophy and theorizing of the classical school. Many scholars began seeing hedonism and utilitarianism, for example, as rather oversimplified philosophies. The Rational Man model of human behavior was criticized.
Positivism is the search for other, multiple factors as the cause of human behavior.
It represents a distinct shift from a focus on law and crime control to the inner workings of the criminal mind and what makes it tick. It's important you understand that positivist criminology is not all about biology or Darwinism. Lombroso only emphasized that part of it because he was trained in medicine. You could just as easily have psychological positivism or sociological positivism, in fact, any discipline could be positivistic. Let's take a look at a couple of Lombroso's pupils who became famous, and then examine some different branches of positivism.