why soak the calamari in buttermilk?
Buttermilk seems to serve as a tenderizer-- I soak fried chicken in it. It also gives a nice coating so flour or bread crumbs will stick.
I believe the main reason seafood is sometimes soaked in milk/buttermilk is to neutralize unwanted fishy smell.
Like Nutcakes says it acts as a tenderizer. There's another benefit if you're frying frying it and coating with self rising flour---or a coating with flour with a base agent like baking soda. The acids in the butter milk will react with the base giving it a light crunchy coating.
Don't despair if you don't keep buttermilk on hand. There's a powered version available in the baking section which is perfectly fine for baking and soaking. In fact, some say it's better than 'cultured' buttermilk as the acid ratio is closer to natural old fashioned buttermilk. You keep it in the freezer after opening in a well sealed container.
Yes, buttermilk has a tenderizing effect because of its acid content. Acids break down proteins, which occur in long, sinuous, complicated structures. A combination of lemon or lime juice and olive oil will have a similar effect, but won't result in that satisfying crunch that Sam1148 describes.