I took a class recently that had a lost of twists to it. Suffice to say it was an area that rarely gets that much attention for myself. The next day, through sheer tenderness (yikes), I had a muse over why that came my way.
When Ayurveda connects with Yoga we look to the asanas from the perspective of the dosha. Twisting is considered beneficial for Pitta due to the tourniquet release of the liver but I reckon there's more than that. Pitta is so straight line in how it views the world. It charges and pushes and can be linear and obvious in it's approach to problem solving.
Twisting looks left and right. It adds periphery and takes in the environment of objects around you. It takes the bigger picture and connects it to your body part. It's good for the eyes too (where Pitta has major stakes) - incorporating eye exercises in a twist can be a double whammy.
In yoga we are used to going inwards, which is that spirit thing, but it can also be used to pay attention to the gross element of the body and Ayurveda is one avenue to do that.