Lynn Sislo wants a clarification of "dissonance", since apparently she just listened to a piece of music described as containing quite a bit of dissonance but which she found beautiful and haunting.
Well, to start with, "dissonance" is a term that has to do with a work's harmonies, and that's it. Here's a good "starter" definition. Unfortunately, the term seems to have accrued a connotation of negativity, so that if we find a work's harmonies unappealing, we complain about "too much dissonance". But in truth, a work can contain a lot of dissonance and still be "beautiful". The canonical example here would probably be the Prelude to Wagner's Tristan und Isolde, which I suspect would be described as beautiful by most sophisticated music lovers. Dissonance does not equal Cacophony.
So what is dissonance? It's what arises when you inject a musical note or notes into a setting in which it doesn't belong. Take a simple chord, a C-major triad. The notes -- C, E, G -- complement each other to form a consonant chord. (Take my word for it.) But if you play that chord and then strike the B-natural just below the C, you'll discover a dissonance: the B and the C clash, and the resulting four-tone chord becomes one of harmonic tension instead of one of harmonic consonance.
Dissonance is actually one of the most powerful tools in the composer's kit. Shifting from dissonance to consonance is a fundamental aspect of musical expression. What's so amazing, though, is that it's often not entirely obvious where the dissonances are, because dissonance does not equal "ugliness". One of the most beautiful pieces I know, Percy Grainger's setting of the Irish Tune from County Derry, contains some highly dissonant chords, but the way that Grainger handles the setting -- with the lushness of the harmonies in the bass voices -- masks the dissonance, so one is never consciously aware of the harmonic tension at work beneath the familiar tune of "Danny Boy".
A lot of times it's hard to tell that dissonance is there. On a piano keyboard, if you strike Middle-C and the B-natural just beneath it at the same time, the two tones create a pretty harsh dissonance: you can hear the two tones clashing against one another, and the effect is one of great tension. However, if you strike instead the C above Middle-C and the B-natural an octave below the one from before, the resulting dissonance is harder to hear, because the distance between the tones is greater. But the dissonance is still there, and it still implies a resolution to consonance.
An interesting question is: Is dissonance essential to musical expression? Could a composer write an interesting work out of nothing but consonant chords? I have my doubts. One thing is certain, though: music can be beautiful and dissonant. In fact, I suspect that since beauty depends on contrast, beauty in music must involve dissonance, to some extent.