A 320kbps constant bit rate song means every second of the song consists of 320kilobits
A 320kbps variable bit rate song means on an average the song contains 320kilobits for every second of the song. The more complex portions of the song are encoded using more bits per second, the less complex portions with fewer bits per second.
For example, a 10 second duration which contains very smooth variations in the amplitude can be encoded using lesser bits; whereas another 10 second duration with extra-fast variations in the music would be encoded using more bits so as to retain more information - thereby giving better fidelity. This is the advantage of a variable bit rate song.
On the other hand, variable bit rate songs are more complicated to encode and decode; so getting your media player to play variable bit rate songs usually forces the decoder and associated software/hardware modules to work at their peak.