As the above posts have noted, there are many possible themes to Bram Stoker’s Dracula. All of them are reasonable and defensible. This is often the case with good literature—it can be experienced and understood on many levels.
To understand Stoker’s central meaning, it’s important to look at how danger is presented in the novel. Where does it come from? What do we know about it? It’s not likely that Stoker was really concerned about the danger posed by vampires. Obviously there is something else Stoker is getting at.
Dracula, as the primary antagonist in the novel, comes from Old World Europe. He represents a deep, dark, and mysterious past—a time and place that the West has lost touch with (if it was ever “in touch” with it in the first place). While the West has made great scientific advances, it has not kept its knowledge of the more primal, natural side of existence. The vampire is able to capitalize on modern man’s ignorance and establish itself in the West, much to the detriment of his neighbors.
With this in mind, we could state the theme as a warning: Forget the past at your own peril.
When Van Helsing saves the day, he does not do so by applying modern science, but by using what he has learned about vampires. Thus, the modern man must learn about the ancient man to successfully defeat him.
Stoker lived in an era when technological innovation was still relatively new and slow moving, at least compared to the whirlwind of invention and change we live in now. Writers like himself, Mary Shelley (Frankenstein), and H. G. Wells (The Time Machine, The Invisible Man) were all concerned about where science would take us if we were not able to foresee the consequences of our expanding knowledge and capabilities. Stoker’s Dracula is a little different than Shelley and Wells in the sense that it emphasizes the need to keep our knowledge of where we come from more than just looking at what scientific advancement will bring.