What does “resolve” mean in the context of music theory?
In a particular key – that is, with a particular set of notes, with one of those notes treated as a “home base” that you return to frequently – each note has particular roles (“functions”, in music theory terminology, as in “functional harmony”).
In C major, for example:
* C, the tonic, is the calm, resolved, relaxed point you come back to after exciting bits.
* D, the major second, is a dissonant and therefore tense note.
* E, the major third, is a stable, relaxed note.
* F, the perfect fourth, is moderately unstable – your ear doesn’t want to stay there too long – but not too dissonant.
* G, the perfect fifth, is very slightly unstable.
* A, the major sixth, is a bit more unstable than the fourth and fifth, but less than the second or seventh.
* And B, the major seventh, is very dissonant.
Each of the dissonant notes – the second and seventh especially, but the sixth, fourth, and even fifth to some extent – wants to jump to a more stable note nearby (in the sense that that jump is pleasing to listen to). The second wants to go down to the tonic, the fourth wants to down to the third or up to the fifth, the sixth wants to go down to the fifth, and the seventh wants to go *up* to the tonic an octave up.
We call these jumps *resolutions*. The dissonant note creates tension, which adds energy and interest, but we don’t want to stay dissonant for too long if we want the music to be nice to listen to. In the same way that we can introduce a plot with conflict in a story, then resolve the conflict at the end, we create tension and then resolve it in a melody or a chord progression.
Chords also have expected resolutions, and the resolutions are usually related to the resolutions of their individual notes. For example, the classic dominant V^7 chord (the notes G, B, D, and F in C major) contains lots of tense notes, and therefore is a tense and unresolved chord. It wants to resolve to the tonic triad (the notes C, E, G).
Like all expectations in music, this is a rule of thumb, not an absolute rule. Even when it does apply, we can play with it in interesting ways. We can delay a resolution to create a strong anticipation or an “oh, come on, just give it to me!” feeling in our listener, or deny one altogether to create a sense of desperation, even frustration. These can be desirable sometimes.
Resolution is when a note or chord changes from dissonance to consonance – from an unstable, tension-heavy sound to one that is more relaxed and stable. Some chords sound pleasant to us (like the classic tonic chord, made of notes 1-3-5 of a major scale), while some sound unpleasant to us (like the dominant, which contains the fifth, seventh, and second/ninth). This is a factor of the intervals between the notes and the relationships between their sound waves – but that’s all beyond ELI5. The idea is that some notes go well with others and some go less well, and some sound *really* weird together.
But that weirdness is part of what makes music interesting. If it always went from pretty chord to pretty chord, it would sound boring. We mix in some dissonant notes in there to make things tense and interesting, but usually come back to a pleasant mix in the end, *resolving* that tension.
Of course, what a pleasant resolution is depends largely on context and preference. A resolution in jazz, for example, might just mean moving from one *very* dissonant chord to a slightly less dissonant chord, because a large part of what makes jazz great is finding enjoyment in those less-traditional sounds. A classical orchestra is more likely to move from a *somewhat* dissonant chord, back to a very pleasant chord to resolve, because classical music (in general) is a bit more likely to use those traditional voicings.