The first thing it accomplishes is removing carbon dioxide from the blood. We blow out CO2 faster than our body creates it, which is true of any hyperventilating breathing exercise, including Kapalbhati. Removing CO2 from the blood makes the blood alkaline, and can cause us to feel light-headed and tingly in the skin. After this practice, we can hold our breath for relatively long periods of time, bringing ourselves into a deeper form of stillness: stillness of breath.
The other benefit of Bhastrika is the way it balances the autonomic nervous system. By utilizing both the abdomen and chest in the breathing (as opposed to Kapalbhati which uses only the abdomen) we alternately stimulate the sympathetic and parasympathetic nervous system. This helps balance the mind and prepare us for meditation.
In the belly, in the chest. Out the chest, out the belly.
