The signal is split into 4 bands, each one covering a certain frequency range, processed and then summed back together.
The advantage to this is that high and and low end ect will respond to compressors quite differently, so for instance you could compress some wild low end a lot without really affecting the high end or mid range.
They are pretty fun at first, but most people sort of get over them eventually. When I use them I usually only use one of the bands and leave the other three inactive. I will use it to compress a certain frequency I am having trouble with.