I don't know the exact / only uses for these, cause you can use things however you want but -
When mastering, for example, you would use a multiband compressor, because you're compressing a whole mix with numerous sounds, and not all the frequencies should be compressed the same. A single compressor would flatten everything out the same and it won't sound good on a whole mix.
If you were just working on one channel, a single band comp. would be fine. But I'm sure you can use them other ways...