I think that dreams don't necessarily mean anything, but can.
Read an article somewhere that said that all night your optical nerves send signals to the brain -- white noise -- and that the sleeping brain can interpret these as images, and build an image or sequence of images around those images from recent memories or, alternatively, from things that you feel in your subconscious.
Sometimes your subconscious knows or understands things that you don't know, and dreams are a way of telling you about it. Sometimes they're not; my wife dreams copiously and remembers them all. Sometimes she'll relate some bizarre dream, and I'll recognize elements of movies we saw the previous night, things we saw on television -- but nothing really meaningful.
But there are many examples of dreams in which the dream is telling the dreamer something he or she already knows, but not consciously. Here are some examples or dreams that influenced scientific and technological discoveries:
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For instance, the German chemist Friedrich Kekulé von Stradonitz, who discovered the atomic structure of benzene, envisioned the closed-carbon shape of the molecule in a dream of a snake grasping its own tail. From this dream he saw carbon molecules in a swirl, finally forming a benzene ring. He had been wrestling with how the benzene molecule could be formed, but had not been able to make it fit from what he knew about valency of the atoms. In another example, Elias Howe dreamt he was in a jungle, surrounded by savages. They lifted their spears toward him, then lowered them. Each spear had a hole in the tip. Howe later invented the sewing machine. This dream inspired him to move the position of the needle's hole from the problematic location of the base to the tip, an aspect of his invention with which he had been struggling.
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http://www.harvard-magazine.com/issues/ja98/02138.html