Alchemy is the process of taking something ordinary and turning it into something extraordinary, sometimes in a way that cannot be explained. It is the precursor to modern chemistry, once practiced in many different parts of the world.
Some alchemists are also mages, but not all. Many see alchemy is simply brewing potions, but historically alchemists were more concerned with transmuting metals (into gold) as well as obtaining the secret to eternal life.
Fun fact: According to the Twenty-Four Histories, many Chinese emperors and nobles over the years died from consumption of ancient Chinese elixirs of immortality made from mercury and arsenic.