Sonority is a way of classifying sounds in language based on how they’re produced, basically how open or closed the various parts of your mouth are when you’re producing them. Language sounds can be placed in a continuum from the really vowel-y vowels, like /a/, to the really consonant-y consonants, like /p/, with fuzzier sounds like /w/ and /n/ somewhere in between. Since I couldn’t find a good explanation online, I wrote one based on how I explain it when I’m teaching.
A note before starting: it will help a LOT if you say every sound that I mention aloud, maybe several times, paying attention to where your mouth is rather than taking my word for it. Whispering or mouthing the sounds is okay but not ideal because you’ll lose some of the distinctions (especially voicing). Just say ‘em out loud: it is a rite of passage for every budding linguist to have their fellow bus passengers or cafe-goers or library patrons look at them in confusion. You’ll be okay.
Let’s start with vowels. Vowel are the most sonorous, because your mouth is as open as possible. If you want to see the most obvious example, try saying aaaaaaahhh like you’re at the dentist. Why does a dentist ask you to say “aaaahhh”? Because they want your mouth to be as open as possible, and that’s what the low back vowel /ɑ/ is going to do. When you say /ɑ/, your jaw is dropped, your lips are spread, your tongue is relaxed at the bottom of your mouth. Sonorous.
Even the other vowels that require a little more constriction are still really sonorous. Let’s try a long /i/ as in cheese: why do people say cheese when taking a picture? Because your lips are spread, your mouth is open but your jaw isn’t dropped very far, and you look like you’re smiling or laughing. And it’s no problem to hold /i/ or /ɑ/ or any of the other vowels for a long time on a single note until you run out of breath. They’re practically designed for singing. (Incidentally, this is sometimes why people describe certain languages like Italian as “musical”: because they have a high ratio of vowels to consonants.)
Linguists often lump all of the vowels together into a single group of the most sonorous sounds, although if you want to you can split them into low vowels like /ɑ/ (most sonorous) > mid vowels like /e/ and /o/ (slightly less sonorous) > high vowels like /i/ and /u/ (even less sonorous).
What happens when you take one of those least-sonorous high vowels and add just a little bit more constriction?
Let’s start with the /i/ in cheese: if you make a really long /i/ and then let yourself stop gradually, you’ll probably hear the /iiiiiii/ turn into a “y” sound as in yes. The IPA symbol for this sound is /j/, which is confusing for English-speakers but it neatly helps remind us that the /j/ sound is really just the little flick at the end of /i/. You also get this effect naturally in words that have /i/ plus another vowel in hiatus, such as cafeteria or Julia. You’ll automatically put a little /j/ in between the /i/ and the /a/. (Well, that final a is actually a schwa but let’s ignore that for here.)
We can do the same thing with /u/ as in boot: if you make a really long /u/ and release it gradually, you’ll probably hear it turn into a /w/ sound. Have you ever wondered why the name for this symbol is double-u not double-v? Well, it’s because its sound is a variant of /u/, not a variant of /v/, and it was originally written “uu” (v and u were the same in Latin anyway). You can also get the /w/ showing up when a /u/ is next to another vowel, as in Padua or Quechua.
So the sounds /j/ and /w/ are almost vowels, but not quite, which means that they’re the next-lowest thing in sonority, and also gives rise to their name semivowels (also known as glides or approximants).
Getting gradually lower in sonority and more closed in the mouth, are a group of sounds known as liquids (sometimes linguists talk about liquids and glides together as approximants, and sometimes they also split liquids into rhotics, or r-like sounds, and laterals, or l-like sounds).
The two liquids in English are /l/ and /r/ (more technically /ɹ/, but since English doesn’t have any other r-like sounds, people sometimes just use plain r since it’s easier to type). If you say /rrrrrr/ you can feel that your mouth is partially constricted but still has a pretty big open space. If you say /llllll/, you’ll actually feel your tongue coming up in the middle to touch the roof of your mouth right behind your teeth, but leaving lots of space open on the sides where the air passes out, hence the name “lateral”. It’s not too hard to hold a note on either /r/ or /l/ for a while.
Now we’re going to take a slight detour into the nose to talk about nasals. Nasal sounds are produced by blocking off air from leaving the mouth entirely (Look, closure!) and instead letting air out the nose. Try saying /mmmmm/ or /nnnnn/ and holding your hand in front of your mouth and nose. You should feel air from your nose, but not from your mouth. So we’ve clearly gotten more closed (and hence less sonorous) than back with the liquids and glides, but there’s still a big open space in your nose where air can pass through, and that means that you can hold a note on /m/ or /n/ (or also /ŋ/ as in sing).
Back to the mouth. What happens if we make a teeny tiny opening with the lips or tongue and allow just a little bit of air through? Well, depending on where in the mouth you make this opening, you could end up with /f/ or /v/ or /s/ or /z/ or /ʃ/ as in she or /ʒ/ as in Asia or /θ/ as in thing or /ð/ as in then or /x/ as in Bach or /h/. These are all known as fricatives, from the friction that this tight constriction forces the air into as it passes out your mouth.
But whoa! What just happened? We used to have only a couple of examples in each category and now we have lots! We have just made an important jump in the sonority hierarchy: the switch from sonorants to obstruents. Sonorants are the whole group of pretty-sonorous sounds, including vowels, glides, liquids, and nasals, while obstruents are the group of not-very-sonorous sounds, including fricatives, affricates, and stops, the last two of which I’ll get to in a sec.
An important difference between sonorants and obstruents is that while sonorants are basically always voiced, obstruents are commonly found in voiceless-voiced pairs, like /s/ and /z/. (Put your hand on your throat and compare the buzzing feeling that you get when you say /zzzz/ with the lack of buzzing when you say /ssss/ — but you’ll always get buzzing, aka voicing, when you say /aaaa/ or /nnnn/. Don’t try this in a whisper. For more on voicing, see here). Being able to use voicing as a parameter means that it’s easy to divide up the obstruents into more types.
So how do we get even more closed than a tiny gap for air? What would happen if we closed our mouths entirely? Obviously, this can’t be the only thing, because if you just close your mouth and ignore your nose, you’ll both a) suffocate and b) not make any sounds. Not so great.
However, it is entirely healthy to close your mouth and trap up the airflow provided that you only do it for a very short period of time, and that’s exactly what this type of sound does. These are known as stops (or plosives) from the idea of stopping the air and creating a little tiny explosion when you finally let your mouth open. Some examples are /p/ and /b/, /t/ and /d/, /k/ and /g/ (notice the voiceless-voiced pairs again!). You can’t get any more closed than literally completely blocked off, so that’s the least sonorous you can get.
But wait! We’ve missed one! I’ve saved affricates for last because they’re basically a combination of a stop plus a fricative: first you completely block off the air, but then you release it slowly to create a fricative (think of the “a” in affricate as standing for “almost” a fricative).
Let’s try making an affricate: start with a /t/ and then rather than quickly letting your tongue leave the roof of your mouth, just let a tiny little bit of air out. Depending on how you point the air, you could end up with either /tsssss/ or /tʃʃʃʃʃʃ/. There isn’t really a proper /ts/ affricate in English (although try tsunami if you pronounce it very carefully) but there is a very robust /tʃ/ affricate which is often spelled “ch” as in chat. If you start with a /d/ and go to a /z/ or /ʒ/, you can get /dz/ which isn’t really found in English or /dʒ/ which is found twice in judge. Sonority-wise, affricates are found between fricatives and stops, which shouldn’t come as a huge surprise.
Final comments: you’ll notice that unlike our sonorants way up above, it’s really hard to hold a note on an obstruent unless you add a vowel. You can make /sssss/ but you can’t sing it. In English, sonorants can also be a syllable on their own (e.g. bottle: bot-l /bɑt.l̩/, or button: but-n /bʌt.n̩/) but you can’t do that with an obstruent.
Further resources: an illustration of the sonority hierarchy, a list of sounds in English and their category, an explanation of voicing, an explanation of vowels in English, some mnemonics for these terms I’ve bolded, and this really elaborate Venn diagram. Even more resources are also found in the phono link round-up in the protolinguist series.