Okay, I skipped ahead in my book and did some refreshing and learning.
Take a look at the International Phonetic Alphabet (IPA) chart: http://www.arts.gla.ac.uk/ipa/images/ipachart.gif (maximize it if it shows up too small to read - it's big.)
On the top and left, you'll see the symbols used to represent atomic sounds, or segmentals: Consonants (top), More Consonants (mid left), Vowels (mid left), and Other Symbols (bottom left). These are the basic building blocks.
On the right, you'll see the symbols used to represent suprasegmentals (mid right) and diacritics (bottom right).
Suprasegmentals are properties that arise from putting the building blocks together. These properties include variations in loudness, duration, and pitch. All three combine to produce differences in the relative amount of stress placed on a syllable, as makes the difference between the noun CONvict and the verb conVICT.
Variations in duration and loudness produce differences in rhythm. My book says that languages sound different "in part because of their characteristic rhythms". That's something that I wouldn't have thought of immediately, but it does ring true.
Variations in pitch create differences in tone. English isn't a tone language, but in other languages, the tone alone can change the meaning of a word. Pitch conveys other information about an utterance, called intonation. For instance, in the way that you would say He saw the show differently if it were a question instead of a statement.
Suprasegmentals also communicate the speaker's attitude and such in various ways. Just taking a look at the symbols for suprasegmentals, you can see that there's a lot of detail to account for.
To add more detail or flexibility than the building blocks permit, diacritics are added. For instance, toot would be plainly written /tut/. In one way of pronouncing toot, there is an extra puff of air (aspiration) following the first /t/; So the first /t/ gets the 'aspirated' symbol: /thut/. The second /t/ is cut off abruptly without an audible release, so it gets the 'no audible release' symbol: /thutL/. (That's not the right symbol, but I haven't figured out a way to add them yet.) You get the idea, I hope. Diacritics allow you to add more detail. And taking a look at how many symbols there are...
I should point out that a single language (AFAIK) won't use all of the symbols in the chart. But I think it's still an impressive amount of variation and detail.