Defined broadly, a visionary, is one who can envision the future. For some groups this can involve the supernatural
The visionary state is achieved via meditation, drugs, lucid dreams, daydreams, or art. One example is Hildegard of Bingen, a 12th century artist/visionary and Catholic saint. Other visionaries in religion are Mohammed, St Bernadette and Joseph Smith (said to have had a vision of and communed with the Angel Gabriel, the Blessed Virgin, and the Angel Moroni respectively).
Extended meanings
A vision can be political, religious, environmental, social, or technological in nature. By extension, a visionary can also be a person with a clear, distinctive, and specific (in some details) vision of the future, usually connected with advances in technology or social/political arrangements. For example, Ted Nelson is referred to as a visionary in connection with the Internet.
Not even the visionary or mystical experience ever lasts very long. It is for art to capture that experience, to offer it to, in the case of literature, its readers; to be, for a secular, materialist culture, some sort of replacement for what the love of god offers in the world of faith.
— Salman Rushdie (b. 1947)
Other visionaries simply imagine what does not yet exist but might some day, as some forms of visioning (or gazing) provide a glimpse into the possible future. Therefore, visioning can mean seeing in a utopian way what does not yet exist on earth—but might exist in another realm—such as the ideal or perfect realm as imagined or thought. Examples are Buckminster Fuller in architecture and design, Malcolm Bricklin in the automobile industry and some of the pioneers of personal computing such as Steve Jobs & Steve Wozniak. Some people use mathematics to make visionary discoveries in the nature of the universe. In that sense, a visionary may also function as a secular prophet. Some visionaries emphasize communication, and some assume a figurehead role in organizing a social group.
In art
Artists may produce work loosely categorized as visionary art for its luminous content and/or for its use of artistic techniques that call for the use of extended powers of perception in the viewer: (e.g. Gustave Moreau, Samuel Palmer, Jean Delville, Ernst Fuchs, the French Symbolist Odilon Redon, Brion Gysin, Max Ernst, Stanley Spencer, Edward Burne Jones, Adolf Wolfli, Fred Sandback, William Blake, Hieronymus Bosch, and Henry Darger).
Visionary art can be incorrectly defined as a category of primitive art (art of those not formally trained) rather than describing people who have used their visions (or dreams) to create their paintings. Salvador Dalí is one artist who would exemplify visionary art that is neither religious nor primitive.
MR. BLAKE,— I received your letter just as I was rushing to Fire Island beach to recover what remained of Margaret Fuller, and read it on the way. That event and its train, as much as anything, have prevented my answering it before. It is wisest to speak when you are spoken to. I will now endeavor to reply, at the risk of having nothing to say.
I find that actual events, notwithstanding the singular prominence which we all allow them, are far less real than the creations of my imagination. They are truly visionary and insignificant,—all that we commonly call life and death,—and affect me less than my dreams. This petty stream which from time to time swells and carries away the mills and bridges of our habitual life, and that mightier stream or ocean on which we securely float,—what makes the difference between them? I have in my pocket a button which I ripped off the coat of the Marquis of Ossoli, on the seashore, the other day. Held up, it intercepts the light,—an actual button,—and yet all the life that it is connected with is less substantial to me, and interests me less, than my faintest dream. Our thoughts are the epochs in our lives: all else is but as a journal of the winds that blew while we were here.
— Henry David Thoreau (1817–1862)