The breathing exercises of the Brotherhood take the form of alternate nostril breathing commonly practised in Hatha Yoga traditions. They are used to develop inner qualities, strengthen the will, calm the nervous system and vitalize the body.
More details can be found in the book ‘A New Earth’ Vol. 13
“Breathing is a form of nutrition and, just as we have to chew our food thoroughly, in the same way, when we breathe we should ‘chew’ the air. When you breathe in you should hold the air in your lungs (which are a kind of stomach) until they have had time to assimilate fully all the nutritional substances it contains. If you expel the air from your lungs almost at once, you reject these substances before your organism has had time to extract the beneficial elements.
But this is not all: you can also draw into yourself substances, forces and particles from the world above, such things as light, peace and an abundance of life-giving elements. When you breathe, therefore, you should seek to draw into yourself the spiritual elements which you most need at the time.”