How psychology became an empirical science in the latter half of the 19th century and broke off from philosophy?

Behaviors and mental processes began to be examined under the lenses of Philosophy and the Natural Sciences. In India, the Buddha considered that thoughts are the products of what we sense and perceive from the environment. In China, Confucius preached that thoughts come from the inside and not from the external world. In the West, Socrates, Plato and Aristotle debated about the nature of the mind. Modern philosopher Rene Descartes, on the other hand, claimed that the body and the mind are separate and distinct from each other.

The word empirical denotes information acquired by means of observation or experimentation. Psychology was a branch of philosophy until the 1870s, when it developed as an independent scientific discipline in Germany and the United States. Today, psychology is largely defined as "the study of behavior and mental processes.” Both metal processes and behaviors can be measured. As a science, Psychology follows systematic methods of observing, describing, predicting and explaining its subject matter. Wilhelm Wundt, considered as the father of modern psychology, was the first who attempted to measure mental processes. In December 1879, at the University of Leipzig, Wundt conducted an experiment measuring the time lag between the instant an auditory stimulus is presented, and the moment the research participant presses the telegraph key to confirm hearing. The central concept of this experiment is the idea that mental processes can be quantified by measuring the time it took for the mind to translate information presented to the body. 

Summary: Psychology became an empirical science when Wilhelm Wundt (who formed the first laboratory of psychological research at the University of Leipzig, Germany ) conducted the first experiment that measured mental processes and behaviors. The act of measuring in the form of empirical methods and observation separated this new form of science from philosophy and marked psychology as an independent field of study.