The Dragon is the Big Bad's top enforcer. Some Dragons are ferocious fighters who leave the heavy thinking to the boss. Others are smart, detail-oriented administrators who oversee the day-to-day running of the evil organization. Either way, defeating the Big Bad almost always requires the hero to overcome the Dragon first. A common but by no means universal theme is to have the Dragon pose a physical challenge to the hero, while the Big Bad poses a mental or moral challenge.
The Dragon will occasionally commit a Heel Face Turn when confronted by the heroes. If he does so, chances are very good that he will end up killing the Big Bad when the heroes cannot bring themselves to do so; often by joining the villain in death as a final act of redemption.
Please note that effectively being the Big Bad's secretary, or just constantly hanging around them is not enough to be a Dragon. Like The Lancer for The Hero, the Dragon is somebody the Big Bad can rely on (or thinks they can rely on) in a time of trouble to step up and beat the living heck out of the Hero, or maybe just take charge for a while, should the Big Bad not be around to do the job.
The Heavy - The "active" villain that drives most of the plot. This is more often the Dragon than the Big Bad, since most authors want to keep the Big Bad in the background and mysterious for most of the story.
The term "dragon" actually originates from folklore where the hero will often end up fighting an actual dragon before even fighting the more intelligent but weaker Big Bad and described as such in "The Hero Of A Thousand Faces", a non-fiction comparison of various fantasy heroes written by Joseph Campbell. Hence, dragons (or stand-ins for them) are often portrayed as a Big Bad's second-in-command.