When you synthesize, you combine two or more things to create something more complex. It's becoming more common for doctors these days to synthesize Eastern and Western approaches to medicine.
While synthesize was first used in 1830, scientists and inventors were doing what it means long before that, mixing stuff together to create new materials and products. Medical researchers chemically synthesize chemicals every day in the lab, hoping to create the next wonder drug. When you write a research paper on a given topic, you must find and synthesize information related to that topic, so you can understand what it means and structure an argument in support of your thesis.