As an English Ph.D., I have to answer this question with a metaphor. For me, the experience of working toward my Ph.D felt like a long, gradual process of building a city in my head. Not an imaginary city exactly, but a figurative one that serves as a conceptual model for everything that I know: what I learned before and during grad school, and what I am learning now. Every day I pave new streets and add new levels onto already-towering skyscrapers. That city is omnitemporal: in it live antebellum Americans, like Herman Melville and Ralph Waldo Emerson and Andrew Jackson and Frederick Douglass. Also, ancient Greeks, like Plato and Socrates. Even mythical figures like Aeneas and Sisyphus make appearances sometimes. The architecture is varied, with Shakespeare's baroque palaces glittering alongside spartan Thoreauvian cabins. The various inhabitants of the city mingle sometimes unpredictably in my imagination, Melville talking to Plato as well as to Kant and to Wordsworth. Vergil talks to Homer, Ovid to Augustus, Martin Luther to Erasmus, Joan Miro to Rene Velazquez, Jane Addams to Andrew Carnegie, Mark Twain to Ulysses S. Grant.
I don't mean to say that my city has only to do with highbrow things. My city has room for, has ways of helping me to make sense of, everything from a Dr. Seuss book that I read to my son, to a Hollywood thriller that I watch while eating ice cream and popcorn. My doctoral studies in English have shaped me into a person who has a rich well of experiences and perspectives to draw upon in interpreting every aspect of my reality--from the ethereal to the mundane.
I won't go on about the things I learned in my program that you'd learn in any decent doctoral program (research, critical thinking, communication and argumentation skills, persistence, etc). What's particular to a humanities program such as English is that you gain a deep, wide, complex sense of human experience. What are the differences and similarities among human beings who live in difference places and times? How do a society's various cultural productions (philosophy, visual arts, literature, political theory, etc) relate to and interact with one another within the zeitgeist? What matters? Why are we here? What is happiness, and what do we gain by striving for it?
What humanities doctoral studies felt like, for me, was five years of intense concentration on the thoughts of other people, writers and thinkers who, though long dead, had recorded their best ideas in the form of novels, essays, treatises, and poems, so that their ideas could outlive them and enrich later generations. Reading the essays and treatises of brilliant long-dead people is the next best thing to raising them from the grave and asking their advice.
I realize I haven't yet said anything about career. I don't think people ought to go through a humanities doctoral program with a rigid and narrow goal of preparing for the professoriate, simply because those jobs no longer exist (even if you come from an Ivy.) Instead, think bigger than that. By the time you finish your doctoral studies (if you decide to go that route), you'll have a city in your head, as well as all the tools you need to keep building onto and populating that city in ways you can't even think of right now. Not to say humanities doctoral studies are for everyone! You have to love reading, and you have to find joy in letting your mind range over ideas for ideas' sake.
How do you conceptualize your own graduate studies? What do you see as typical of graduate studies in general, and what is unique to your discipline?