Years ago when just beginning the practice I researched Ujjayi breathing and found these two excerpts deepened and enhanced my practice.

May they inspire and direct your practice as they have and do mine!

Source: ASTANGA YOGA BY SRI K PATTABHI JOIS AND LINO MIELE, ASTANGA RESEARCH INSTITUTE MYSORE INDIA, PUBLISHED BY LINO MIELE, 1999, ITALY.

When breath control is correct mind control is possible. Breath: the continuity of deep, even breathing cannot be over emphasized in the Astanga Yoga system. When breath feeds action, and action feeds posture, each movement becomes gentle, precise and perfectly steady. According to the teaching of Sri T. Krishnamacharya and Sri K. Pattabhi Jois, “Breath is Life”. Breath is our most fundamental and vital act and holds a divine essence; exhalation a movement towards God, and inhalation an inspiration from God.

 

Source: UJJAYI BREATH FROM: ASHTANGA YOGA –THE PRACTICE MANUAL BY DAVID SWENSON-1999 

The main idea is to create rhythm in the breath and ride it gracefully throughout the practice. This sound becomes a mantra to set the mind in focus. We must learn to listen to the breath. It is the guide, which will tell us the quality of the practice. If we apply too much effort, the breath will become constricted or forced. With too little effort, the ujjayi breath may be drowned out by the sound of our own thoughts. Maintain awareness upon your breath and every moment becomes a meditation.