The plain and boring technical definition of a dream is: a series of images, thoughts, and emotions that a person experiences in their mind as they sleep (particular during the stage of REM, or rapid eye movement). A dream is a a result of neurological processes that are extremely difficult for the scientific and medical community to understand. Thus, the mysterious nature of dreams has paved the way for widespread speculation about what dreams mean.
Scientists might be concerned with what dreams are and what causes them, but the layman tends to be more curious as to their meaning. There is some logical and compelling evidence for what the evolutionary purpose of dreams might be, but dreams still remains a mystifying and fascinating topic of discussion, largely made up of conjecture that has some of its roots in religious and mythical beliefs from past centuries.
It is estimated that at least six years of an average person's life is spent in the dream state. So it's natural for one to not let those years to go to waste – what can we learn from dreams? What can we do with them?
Whether you have a spiritual take on dreams or a more scientific one, studying their meaning can be very useful. Perhaps you think a dream will predict your future or perhaps you think it simply holds the keys to what's going on in your subconscious – whatever the case, it's interesting and not necessarily futile to examine the meaning of dreams.
In the late 19th century, Sigmund Freud introduced the idea that dreams simply were a manifestation of a dreamer's real-world desires, which were then affected by the dreamer's natural, physiological activity and sleeping environment.
Modern psychologist Joe Griffin theorized that dreams simply fulfill a person's expectations for the day. For example, if a person in waking life expected or intensely hoped to complete a task (like laundry) or say something important to their spouse, etc, but didn't follow through with an expectation, they may dream about performing such actions (in metaphorical ways) and thus arise the next morning without feeling regretful or anxious. The fact that those who are depressed tend to dream more than those who aren't, lends a lot of credence to this theory, which is widely taken advantage of by therapists who want to unlock their patients inner demons and worries.
Professor Michel Jouvet, who has researched experimental neurobiology, believes that dreams actively engage a dreamer's brain and help it learn how to react to potential real-world situations so that when the dreamer awakens, they are more prepared for the real world. If you agree with Jouvet's theory, you think of the dream world as a vast practice field.
Other theories hold that dreams can bring to life past memories, some that may even be buried deep into the subconscious. Again, therapists often use dreams as clues to a patient's troubles. Abused children, for instance, often suffer from intense nightmares.
Religious texts often deem the origin of dreams as paranormal. For example, there are more than a handful of biblical accounts in the New and Old Testament in which people were delivered a message from God in a dream.
Carl Jung, the founder of analytical psychology, built on a lot of Freud's ideas and he agreed that dreams were the conscious and unconscious mind interacting. Both Freud and Jung believed that unconscious brain activity, brought to light in dreams, reveal a lot about human psychology and an individual dreamer's desires, fears, and perception of self.
Every society and culture gives meaning to real-world images and the like. So this is where people really have fun analyzing dreams. But this is strange territory that has hardly any bass in science. For example, have you ever heard that if you dream about your teeth falling out, you're likely stressing about money problems? This dream meaning has been determined by trends in dreaming, rather than any real science. Why people share dreams in common, like falling or teeth falling out, is unknown, but if enough people dream about a specific event, one can compare what those people had in common in their waking life and thus speculate about what the meaning of the shared dream was. Moreover, studies have shown that those who dream about committing an action they are trying to stop in their waking life, like drinking alcohol or smoking cigarettes, are actually less likely to commit the action in real life. But one cannot jump to the conclusion that whenever a person who tries to quit smoking dreams about taking a puff, that means they are cured of their addiction. It's merely helpful to see a common correlation and use it to then examine potential causes.
Dream meanings are also often understood as metaphors and just as one can analyze and interpret a poem, they can do the same for a dream. But this is probably one of the least sensible ways to analyze a dream, as dream interpretation will be more influenced by ideas of culture and society rather than scientific logic.
There are a bunch of other theories about what dreams mean, and it's possible dreams don't have any one specific meaning, but are simply a product of a very complicated neurological process.