At least since Joseph divined the meaning of Pharaoh's dream of seven fat cattle and seven thin cattle -- saying it presaged seen fat years and seven lean years -- people have been trying to figure out what both dreams in general and particular dreams mean.
Penelope in the Odyssey distinguished dreams entering via the Gate of Ivory and the Gate of Horn.
Stranger, dreams verily are baffling and unclear of meaning, and in no wise do they find fulfilment in all things for men. For two are the gates of shadowy dreams, and one is fashioned of horn and one of ivory. Those dreams that pass through the gate of sawn ivory deceive men, bringing words that find no fulfilment. But those that come forth through the gate of polished horn bring true issues to pass, when any mortal sees them.
Even today, in our skeptical and supposedly rational times, simple-minded "1,000 Dreams Interpreted"–type books find an eager market.
Of course, more-sophisticated minds have theorized about what dreams signify. Most famous was Sigmund Freud. His theory of dreams, argued in thousands of his and his followers' pages, was that dreams represented an outlet for suppressed wishes, usually in disguise. Probably Freudian dream theory was essentially a derivative of his overall idea of the mind. His brand of psychoanalysis was based on the notion of an unconscious seething with censored drives.
Freud's wish-fulfillment dream theory seems prima facie ridiculous. How to explain nightmares? Do we have secret wishes to be lost, mute, threatened, humiliated? The Freudians had an answer: even in dreams, the censor was still at work -- sweets had to be disguised as slime. When I was in college I read an account of Freudian psychology by his disciple Ernest Jones. As I recall, he gave an example of a dream in which the dreamer plunged a knife into someone's chest. He explained that the dreamer didn't actually want to stab someone. The dream was a metaphor. The knife was a phallic symbol. Sticking it in the chest was another way of working around the censor: it was displaced.
Even then this struck me as making the phenomenology of dreams fit a preconceived theory. Apparently lots of people feel the same way. Outside of the Freudian psychoanalytic priesthood (there are still analysts who practice classical Freudian technique), few take most of his ideas seriously now -- although he is justly credited with discovering the power of the unconscious. His wish-fulfillment dream hypothesis, in my view, is meaningless because unfalsifiable as long as anything can be interpreted in its terms.
One of the most interesting dream theories was Carl Jung's. At least in his case, it looks like his larger framework -- especially the idea of archetypes -- was derived partly from dreams, rather than his notion of dreams being an outgrowth of his psychoanalytic theory. If there is such a thing as archetypes, and he makes a good case, it's reasonable to believe that they show up in dreams.
But Jung, like Freud, turned reductionist. By his later years, he seemed to perceive everything as archetypal; even UFOs.
Psychical research has a rich history of dream study. (This is a tiny fraction of the literature.) Dreams apparently -- at times -- deliver precognitive (example) and clairvoyant (example) knowledge. Then there is lucid dreaming, in which people know they are dreaming and can write the "script" for the dream. Reportedly there are quite a few who dream lucidly sometimes.
Religious mystics have often cited dreams associated with their metaphysical experiences.
My suspicion is that most of these explanations of dream meaning account for a few dreams, but not many. From an epistemological standpoint, most dreams are no different from ordinary waking experience: occasionally significant, mostly just phenomena. Not that they're "junk," unless you consider everyday experience junk; but of no special or unique importance.
I can remember one dream in my entire life that seemed to me then, and still seems insofar as I can recapture the feeling, as possibly having a spiritual quality. I couldn't describe it to you, can hardly describe it to myself in words.
And then there is -- I have to borrow the expression from Rider Haggard's book title -- She.
She visits me in dreams from time to time.
I don't know her name or who she is. She is Love and Beauty and an ideal. She looks different on different visits but I recognize her, usually during the dream itself, sometimes afterward.
She has nothing to do with eroticism. Her meaning is greater. But I don't know what.