Multiband compression works by splitting the incoming audio into different bands, much like your bass/mid/treble controls on your EQ only works on bass/mid/treble parts of the frequency range. Compression is then applied to only those frequencies and then they are summed together.

There is no pitch shifting in multiband compression - pitch shifting involves moving the frequency up or down by a number of cents, semitones, octaves etc. It's the effect used to get the "chipmonk" voice (high-pitch and squeaky) where a normal voice is fed into a pitch shifter and it is shifted up or down. It is also how harmonisers work, where they work out the frequency you're singing at and shift it up 7 notes (or an arbitrary amount) so you can sing and get a harmony of yourself.