What is synthetic chemistry?

Simply put, synthetic chemistry is the study/practice of chemistry as related to synthesizing (fancy word for "making") new chemicals. If someone is a synthetic chemist, they focus their efforts on making "stuff." It is the variability of the word "stuff" that makes synthetic chemistry different across the spectrum.

For example, a pharmaceutical chemist (a chemist who makes drugs) is a synthetic chemist. A polymer chemist (a chemist who makes polymers such as Rayon or Nylon) is a synthetic chemist.

Synthetic chemistry is a very broad term but focuses of the actual making new or variations of existing chemical stuffs.