Multiband compression is dynamic - it responds to changes in the audio. Parametric EQ is static - no matter how the audio evolves, it always cuts/boosts the same frequencies by the same amount.
Consider a real example - deessing a vocal. You could try using a parametric EQ to cut the sibilant frequencies, but this would probably make for a very dull sounding vocal. You could try "riding the fader" to only cut the EQ during the problem bits, but that's too much like hard work.
Instead, take a multiband compressor, home in on the sibilant frequencies with one of the bands, and set say a -9dB threshold with 2:1 compression. When the vocal is OK (no sibilance) the threshold is not exceeded, and the vocal passes through unmodified. When sibilance happens, the threshold is crossed and the compressor dynamically cuts the volume of the offending frequencies. Effectively, it rides the EQ fader for you.
Same thing applies to, say, limiting a bass line which occasionally peaks in volume in a mix. If you use parametric EQ, you would simply be cutting the bass response of the whole track. Use a multiband compressor instead, and it only cuts the bass volume when the bassist gets too loud.
Multiband compressors have lots of other useful applications, but I think this covers your specific question.
Cheers,
Dave
www.db-audioware.com