The meaning of music is hard to capture in words. Let's try some ideas anyway!
The brain bug
The brain has a natural ability to extract patterns from all the stimulus. It's a fact that we like the music that has some patterns: that is not very monotonic (boring) but not very random either, so we can continuously learn some new patterns. Somehow the brain has the illusion that it continuously learns in an accelerated rate by listening music. So music could be considered a small addiction at the first analysis.
The social binding
Even if such "bug" may exists, music took an additional, very important, role in human society. The music expresses feeling and makes us feel connected, stimulating empathy. We feel that others have feelings similar to ours, that we are more alike than different.
The brain muscle flexing
Some studies shows improvements in brain thinking capacity by listening music. I'm not so sure that music improves thinking capacity on the short time. However, sufficient complex music is likely that, on the long term, it improves the memory and pattern recognition. This is even more evident for people that learns to play a music instrument.
The brain "electrical" grounding
I often realized that music activates parts of my brain that are not active in the usual life circumstances. It's like there are electric charges accumulated in my brain and music is able to access them and ecologically discharge. Brain scans showed that good music tend to activate many brain regions. This activation could trigger synapses close to activation, discharging the potential (actually chemical, not electrical). The effect can be like a good sleep with dreams, less interferences from these regions of brain with the conscious thinking. Unlike sleep, I think music is more likely to discharge emotional stress accumulated in the long term memory - that is less likely to be discharged by sleep.
Bottom line
Music is a great expression of the human spirit. It will always escape from definitions, because it is very intimately connected with the human brain physiology and culture. If dogs would have music, it would not be like our music. It's about a wide range of timeouts, like how much time you would wait until the next note to "solve" the tension. This is why we need good and talented musicians to transcript a written melody and we cannot just play it by a computer.
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