Psychologists seem to fall into two groups regarding dreams. The first group believes that dreams have no real purpose; while the second group believes they do have a purpose, although this group cannot reach a consensus on what the purpose might be.
Sigmund Freud is probably the most famous of the dream theorists. He believed that dreams helped to preserve sleep by keeping individuals from waking as a result of physical urges such as needing to go to the bathroom or feeling hungry. This theory was developed before the knowledge of REM sleep.
Carl Jung, an early follower of Freud, broke away from that theory to develop one about dreams compensating for under-developed areas of our personalities. This theory
was disproved by Calvin Hall who did a study that shows that dreams are a continuation of our waking thoughts and behaviors.
Other dream theorists claim that the purpose of dreams is for problem solving. The thought is that dreams can deal with problems that we are unable to solve consciously, so when we dream about it our unconscious minds can find a solution to the problem. There is no real proof that this is the case, but this is tied to cultural lore that dreams have uses. In recent years new claims have been made about dreams, but they are not tied to any particular theory or researchers.
Dreams do have meaning though. Dreams are usually related to the age, sex, and cultural experiences of the dreamer and can be very revealing about their thought processes. Analyzing 75 to 100 dreams can give you a psychological profile of the person and can be almost as individualized and accurate as fingerprints to an individual.