It's a broad question, but perhaps helped somewhat by the stated purpose of world-building. As I understand it, the OP doesn't necessarily need a historical perspective of all the various styles and genres of music or how their composed, but rather a high-level overview of music that can provide a jumping off point for their own creativity. But even that is necessarily going to be lengthy and jargon-packed.
By the way... have you seen http://worldbuilding.stackexchange.com? (nevermind: I just checked your profile, and noticed that you've been there quite a bit).
From a very high level, music can be thought of as sounds distributed through time. (Note: this is not a sufficient definition -- there are certainly sounds distributed through time that are not music -- but this definition is deliberately overly-broad so as too be as inclusive as possible for the purpose of world-building).
Now right away, we see there are two aspects to music: the sounds that are being made, and the way those sounds are distributed through time. The way sounds are distributed through time is often referred to as the rhythm. There's often some sort of steady repeating "pulse" or "beat" to which the timing of other sounds can be referenced. Varying this underlying pulse can shift the music in a whole new direction, but doing that too frequently can become chaotic, distracting, or confusing. The brains of the performers and listeners tend to entrain to a specific beat, and gets surprised if that changes too much or too often.
If we move on to looking at sounds, there are basically two kinds: those that have some definite pitch to them (like voice, violin, flute, piano, guitar, etc...), and those that don't have a pitch (essentially drums, and other forms of unpitched percussion). Music can consist entirely of just one or the other, or there can be a mixture of the two.
Assuming you do include pitched instruments, than you have to start asking what pitches can be used. While some instruments (like the voice, unfretted string instruments, and the theramin) are capable of producing any variation of pitch within a continuous range, other instruments (like fretted string instruments, harps, woodwinds, and keyboards) are limited to a discrete set of pitches. The set of pitches you decide to use is called your scale, which forms the building blocks of all your possible melodies (melody here assumes that you are using at least some pitched instruments). In a world-building scenario, there's no a priori reason to stick to a well-known western musical scale (like pentatonic, diatonic, or chromatic); there are any number of so-called "xenharmonic" scales possible, most of which will contain microtonal intervals and will likely sound out-of-tune to our western-tuned ears. I know I just threw out a bunch of jargon, but these are, I think, interesting places that a world-builder could go if they wanted truly exotic-sounding music. The big downside is that there's a lot of theory involved to understand what's going on, and probably special software required just to hear what it sounds like.
At this point, we have rhythms (the distribution through time) and melodies (a series of pitches from a scale, if you have them). For a lot of world music, this may be all you need; there's plenty of non-western music that doesn't really have a proper "harmony" per se. If rhythm is the "horizontal (temporal) aspect of combining sounds, than harmony is the "vertical" (non-temporal) aspect of combining simultaneous pitches. The rules of creating harmony are something very particular to western music and to the way its scales are formed from the overtone series. In short, you'll want to think about which notes of the scale sound good together (consonance), and which sound... less good together (dissonance). The later may be used to provide tension, but often only in specifically managed contexts (with proper preparation and resolution). Historically, these definitions can be thought of as a sliding scale, with musical tastes generally becoming more accepting of stronger dissonances in a greater number of contexts. Larger combinations of multiple consonances (and dissonances) form chords, but that is another concept that historically originated in late in western music, around the period of 1550-1650, and may not be needed to fit your own world's music. Besides, if you use a different type of scale, you may end up with completely different types of chords anyway.
Once you start combining notes, you'll need to start thinking about the music's texture. If everyone's singing the same melody without any harmony, the texture is monophonic (think of your typical medieval chant). Sometimes monophony can be supported by simple drones as well, since those don't really add independent parts. If there are multiple parts that have some measure of independence to them, the music is said to be polyphonic (think of a Renaissance madrigal, or a Baroque fugue). If there are multiple parts, but one melody part is clearly dominant, and the other parts merely support it harmonically, the texture is said to be homophonic (simple four-part church chorales, for example). Note that polyphonic and homophonic music both have multiple parts, but the difference is in the independence of those parts. The texture of a piece does not have to remain fixed. You might alternate a monophonic chant with a polyphonic refrain.
Finally, we come to structure. Structure refers to how the overall piece is laid out. Think of this like your rising/falling plot in a story, or a three-act structure in the film. Like rhythm, this refers to how elements of the music are distributed through time. But where rhythm looks at individual sounds with reference to some continuous pulse, structure takes a higher level view of entire phrases and whole sections throughout the entirety of the piece. The difference is not unlike that between the distribution of words on a printed page vs. the distribution of chapters in a book. In music, structure is built around two opposite principles: repetition and contrast. A fruitful combination of these two ideas leads to not-quite-exact-repetitions: elaborations and variations.
- A piece with all contrast, and no repetition is said to be through-composed. If each letter represents a section of the piece, it's structure looks something like: ABCDE...
- A piece with all repetition and no contrast is said to be strophic (consisting of verses, like a hymn). It's structure is: AAAAA...
- A piece consisting of variations on a theme (using superscripts to denote variations of the original structure), will have a structure that looks like AA1A2A3...
- A piece with two contrasting sections is said to have a binary structure. In the simplest case, this looks like AB. However, each of these sections might be repeated (AABB), or you might have the entire structure repeated (ABABAB...) which looks like a modern verse/chorus form.
- A ternary structure is similar to binary, but has a repetition (or variation) of the original section at the end: ABA.
- A piece that alternates a repeating section (a refrain) with multiple contrasting sections is said to have a rondo form: ABACADA...
I could continue on with other forms (for example, sonata-allegro form, which is surprisingly similar to verse/chorus/bridge form, both having the basic form of ABABCAB) but it would possibly start to get too specific to western music. I've shown enough here to show the basic principles, and everything else is combinations and elaborations of those principles.
Hopefully I've given you a high enough overview to give you a taste of what's possible and how various elements can be combined.