Dracula has been interpreted a myriad of ways over the years, with many focusing on its depiction of women and sexuality or simply describing it as a battle between good and evil. And these are valid ways to look at the book, but one significant message of Dracula is its emphasis on contrasting the past and the present, the ancient world clashing against modernity.
The conflict between the ancient past and the modern world was nothing new in gothic literature, but Dracula especially emphasizes it. Modern technologies connect the world through telegraphs and telephones and allow people to survive illnesses that killed people long ago, yet the vampire is still able to wreak havoc on the populace. Modern blood transfusions are unable to rescue Lucy from becoming one of the undead, and only ancient methods of destroying vampires can save Mina's soul from corruption. Even Jonathan Harker, long before he learns his host is a vampire, can sense the power the ancients still hold over the modern world:
Here I am, sitting at a little oak table where in old times possibly some fair lady sat to pen, with much thought and many blushes, her ill-spelt love letter, and writing in my diary in shorthand all that has happened since I closed it last. It is the nineteenth century up-to-date with a vengeance. And yet, unless my senses deceive me, the old centuries had, and have, powers of their own which mere "modernity" cannot kill.
(A contextual note: shorthand was considered new-fangled at the time of Stoker's writing, hence why Jonathan deems it "up-to-date with a vengeance," compared to a longer, old-fashioned love letter.)
There is a greater meaning to the ancient vampire's lingering power: going back to the view of Dracula as a classic tale of good and evil, Dracula represents the ultimate in evil: selfish, cruel, violent, and corrupt. Because Dracula still has power even in the modern world, Stoker is similarly suggesting evil is something modern manners and technology cannot simply dispel.
The main themes of Dracula are as old as time: the battle between good and evil, the question of life and death and what people would be willing to do to live forever etc. The novel isn't exactly trying to teach the reader a lesson, as the main story is fairly simple, but it raises important questions about the characters and the situations they're put in.
Count Dracula as the central character symbolizes something dark, but also very human. At the beginning of the novel, Dracula is already a vampire, a supernatural being, but it's suggested that he was human once. The question of whether he chose to become a vampire or not is not clearly answered, but it's clear that he does not object to the toll it takes. On the contrary, he seems to torture Jonathan Harker with glee and has no determinable guilt concerning his actions. With that, Dracula serves as an example of a being who is willing to kill to be immortal. Not just that, but a vampire must go on killing for their entire existence, since they always need more blood. The other characters are horrified by it, but a few admit slight temptation. What would any person be willing to do if they could save themselves from dying? Dracula wasn't, contrary to popular belief, the first vampire story and it certainly wasn't the last. Everlasting life is a theme many authors have turned to. The message, if there is any, seems to be that to get something so precious - immortality - a person has to be prepared to sacrifice everything.
There are also those who stand up to Dracula, although it isn't as easy for them as it should be. Finding methods to kill a supernatural being is one thing, but there are also choices along the way that horrify them. For example, when professor Van Helsing determines that they must drive a stake through Lucy's heart to save her, the others refuse at first. The thought of killing something that is already dead is still killing to them. Not to mention the religious concerns. In that way, the novel also deals with the question of what people are prepared to do if they choose to fight a vampire. Merely resisting a vampire isn't enough, as difficult as that may be with Dracula's powers of mind control. Almost all of the characters need to step out of their comfort zone - into superstition, into what seems like madness at first - to combat the vampire.
These are, of course, only a few interpretations and themes of Dracula. The novel can be read in many ways and has several layers not discussed here.
The most obvious less to me is the nature of good and evil. A person can try to be good, but be “infected” by evil, just as metaphorically a person becomes infected as a vampire. Then you live a cursed life, rather than a life of eternal bliss.
There are a number of interpretations we might make if we read the story thematically or symbolically.
I'd like to say that the Dracula story functions as a counter-part to our notions of idealized eternal life. What if we were granted our wish to live a human life forever, but we must become a monster in the process?
Taking this as the comment, we can see the story as an expression of the idea that human life is only "human" within its natural limits.