getting the compressor to "breathe" with the music

[cris is bliss]

I've read that the compression used on the overall mix should breathe in time with the music. How is that technique achieved?

[resolectric]

Adjust Attack and Release settings accordingly with the music's rhythm.

Imagine applying compression to maximize volume on a song where the parts are accentuated as follows (this would be a 4/4):

TAM tam tam tam... TAM tam tam tam...

If you apply a fast Attack and a fast Release you may get:
tam TAM tam tam... tam TAM tam tam

If you apply a fast attack and a slow release you may get:
tam tam TAM tam... tam tam TAM tam...

Of course, this all depends on the song's Tempo, the rhythm texture and the accentuation of parts.
You have to listen when applying compression. Compare with and without to see if you are, in any way, damaging the accentuation and the dynamics of the musical parts and adjust Attack and Release settings for the most musical result.