Based on the title of the novel, you'd probably assume that the whole book is about Anna Karenina. Ha! Tolstoy is way too crafty for that.
While Anna is one focus of Tolstoy's intense psychological analysis, the novel is about a lot more than just one woman. It's also got a series of polemics (a.k.a. hyper-intense arguments) about a variety of social, political, and philosophical issues.
Home Is Where The Drama Is
As Richard Pevear points out in his introduction to his and Larissa Volokhonsky's translation of Anna Karenina, one of the cornerstones of this novel is its genre. Tolstoy describes Anna Karenina as his first novel (even though he started the even-more-massive War and Peace first), because his earlier books were long stories and historical chronicles. Tolstoy views the rules of the traditional novel—a long piece of prose fiction focusing primarily on a small group of central characters—as a challenge to his wandering writing style.
Typical Tolstoy. Starts writing a novel as a challenge... and ends up penning one of the greatest novels ever written.
For Tolstoy (argues Pevear), the novel is specifically the genre for domestic drama. Thus, the novel form is the perfect showcase for Tolstoy's extended contemplation of modern versus traditional family values—as focused through the character of Anna Karenina.
So Why Not Call It A Bunch Of Unhappy Russians Arguing?
Still, you may well ask, what does all this stuff (domestic drama, crazy polemics, etc) have to do with the title? Well, one aspect of the 19th Century novel is that it often connects its merry band of characters through their relations to a single protagonist—think Jane Eyre, Madame Bovary, or Oliver Twist.
What's more, by naming the novel Anna Karenina, Tolstoy is effectively saying that the life of this one woman is worth eight hundred pages of storytelling. Her concerns are the mundane (i.e., day-to-day) cares of a woman caught in a bad marriage and in love with another man. This is ordinary stuff, the problems that anyone might face.
Yet, Tolstoy narrates Anna's life with the care that previous authors might have used to celebrate someone like George Washington or Queen Elizabeth or Odysseus. By turning an ordinary person into the hero of his novel, Tolstoy makes the details of Anna Karenina's life into tragedy as painful as anything you'll find in Hamlet or Oedipus the King. The title of the novel alone tells us that Anna Karenina (the person) is something special.
And Tolstoy's genius is so massive that once Tolstoy gets it into his skull to make Anna K a special someone, he totally delivers.