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 is an integral part of the Five-Bad Band dynamic. If there's a Quirky Miniboss Squad, the Dragon is often the unofficial leader.
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 Man Behind the Man - When the Dragon has his or her own Dragon, The Man Behind the Man is the Bigger Bad.
My Master, Right or Wrong - When the Dragon does things he doesn't agree with out of loyalty to the Big Bad. They will often be an Anti-Villain in this case.
Noble Top Enforcer - When the Dragon is an Anti-Villain that is considerably more virtuous than his master. Likely to turn on the Big Bad if their actions piss him off enough.
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.