On amud beis we find Rav Yannai troubled by a dream that he had, of a splintered reed. He the dream to mean that he made a halakhic mistake, by relying on a weak proof. Rav Chiyyah comforted him, by reading the dream as the opposite, implying a broken reed is humble and therefore merits to see the truth:

How did the Gemara treat dreams?  Are they prophetic, or to be ignored as the result of random images and impulses firing during the night?  The Gemara has conflicting teachings about dreams.  On the one hand, Berachos 57b states that dreams are 1/60 of a prophecy, as well as our gemara, where a dream is taken quite seriously by Rav Yannai.  On the other hand, we have a Gemara (Sanhedrin 30a) which rules that dreams have no legal significance. Thus if a man dreams that his father sequestered maaser sheni money in a particular place, he has no obligation to regard it as sacred. There is a similar Gemara in Gittin (52a) that also discounts the legal implication of a dream.  So what is the correct attitude?

There is a responsum of the Tashbetz (II:128 Rav Shimon Tzemach ben Duran 1361–1444) which dealt with an odd situation where one person dreamed that the entire congregation would be placed in heavenly cherem unless they all fasted.  The local rabbi followed the dream and they treated it as a full ta’anis tzibbur, including reciting the traditional blessings.  He was asked to rule post facto if this was proper:

He rules that in this case, the people could choose to pay attention to this man’s dream or not, as it was his dream, not theirs.  If they did so, it would be better for it to be considered an individual fast without blessings and not a public fast, as there was no clear evidence of its veracity. If, on the other hand, a person has a dream of bad portents for himself, he should take it seriously and fast as is described in Gemara Shabbos (11a).. 

The Tashbetz goes on to explain his reasoning, the Gemara Berachos (55b) actually raises the contradictions about the Torah’s attitudes toward dreams itself:

Rava raised a contradiction between these verses: On the one hand, it is written: “I speak with him in a dream”; and on the other hand, it is written: “And the dreams speak falsely.” The Gemara resolves this contradiction: This is not difficult because there are two types of dreams. Here, the verse, “I speak with him in a dream,” refers to dreams that come by means of an angel; here, the verse, “And the dreams speak falsely,” refers to dreams that come by means of a demon.

Based on the Rambam’s ideas about the intellect and the soul, which is that our soul connects to God through intellectual harmony and resonance. That is, the more we are refined and wise in action and thought, the more we are able to achieve greater conjunction with the will of God, and can have prophecy on a larger scale, or perhaps small divinely inspired intuitions and insights on a smaller scale. (For more on this see Guide for the Perplexed II:45 and III:51).  If you will, when our souls are at a proper level of harmony with God’s will, we “link up with cloud”. 

In the Rambam’s theology, angels and demons are metaphors for spiritual agencies within us, as well as outside of us.  Thus, when one is asleep and his intellectual processing is subdued, his imagination takes over.  His imagination may be stimulated by purely physical desires and stimuli or it may be influenced by spiritual emanations and non-verbal intuitions that are expressed by the symbolic process of the imagination. Depending on the intellectual and moral development of the person, and their state of mind when dreaming, the dreams could be merely stemming from demons (the physical stimuli) or angels (spiritual stimuli).

Therefore, when it comes to legal matters, dreams are not considered proof of facts, however when it comes to personal spiritual matters, it is best to err on the side of safety but you cannot compel someone to do so based on a dream you had about the other person.

Dream interpretation is one of the best examples where psychology and mysticism intersect and how each discipline tries to explain the process of how non-verbal, symbolic ideas pertain to the function of the soul.