Multi-bands rock.
As a mixing tool, you can use it as a de-esser or a de-rumbler.
As a mastering tool, it can be used to give your mix better balance . . . or you can use it to bring out a given instrument or tone it down.
I'm sure you already know the basics. So this explanation is more for the newbs.
Don't say I don't help you guys out.

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When you EQ something, you're completely "altering" the frequency makeup of a given sound. When you use a multiband compressor, you're merely "shaping" it.
Here's an example: I was just mixing something earlier that had a lot of accoustic guitars mixed in with a lot of other stuff. Naturally, I don't need all the acoustic's low end muddying things up and burying it in the mix. . . . but I still want it to sound "full," as it isn't in the mix just for texture . . . it has a definite purpose in a dark-sounding song.
Just like a normal compressor can be set to put limitations on how loud something gets, the multiband compressor sets boundaries on how "boomy" my accoustic guitars are allowed to get while they play.
Guitars have a dynamic element to them. Their frequency content will change throughout the song. There will be parts where it will get "too" full (and bury itself in the mix) -- like when a powerful chord is played or the "E" string is hit aggressively. And there will also be parts where the playing is more delicate (as in more finger picking on the higher strings).
Normal dynamic compression is like having someone with super-fast ears and hands turning the volume knob up and down when something gets too loud or too soft. The multiband compressor is the same thing, but only you have someone working the eq knobs instead of the volume . . . and he's very flexible.
Now picture this dude working a low-shelf eq on my accoustic guitars starting at about 300 hz. His job is to turn the low eq down a bit every time the lower power chords are played. This will help the guitar to sit better in the mix . . . it will also allow the bass and snare to be heard better without interference, and it will prevent mud. Now, during the more delicate parts where there's less boom, he turns it back up. This helps prevent the accoustic from getting all thin and twangy-sounding - a danger you run in to when simply cutting the lows and boosting the highs with eq.
You can also have him work the high treble control, waiting to turn it down every time there's a really grating crash cymbal hit or "sssssss" coming out of the singer's mouth . . . then turning it back up after it's done. Your only other alternative would be to cut the high EQ, which would certainly tame the errant esses and cymbal crashes, but it would also effect the rest of the track, making it sound duller and less definined when the "ssss" aren't going on.
This is my over-simplified explanation, and again, it is more for the newbs.
To the more advanced, my suggestion would be to experiment. Use it instead of eq to cut or shelve frequencies from time to time, and see if you like the results better. Use it to tame anything there's too much of that is recurring in your mix. Like if your snare is too loud, compress around 200hz or wherever the bulk of the snare's action lies. Compress around 4 khz or so if you've got a crazy, out-of-control crash cymbal. Ditto for the kick at around 64-80 hz.
You can also use it to BRING OUT things much more effectively than with EQ. Particularly, I have rescued lost bass guitars before with them. Anyone familiar with Waves'
maxx bass plugin -- that's basically a glorified multiband comp specifically taylored to be bring out more bass. Again, it's more of a thing you just have to experiment with and learn.