Here is a clear and informative explanation of the tristhana method from the K Pattabhi Jois Ashtanga Yoga Institute website:
“[Tristhana] means the three places of attention or action: posture, breathing system and looking place. These three are very important for yoga practice and cover three levels of purification: the body, nervous system and mind. They are always performed in conjunction with each other.
“Asanas purify, strengthen and give flexibility to the body. Breathing is rechaka and puraka, that means inhale and exhale. Both the inhale and exhale should be steady and even, the length of the inhale should be the same length as the exhale. Breathing in this manner purifies the nervous system. Dristhi is the place where you look while in the asana. There are nine dristhis: the nose, between the eyebrows, navel, thumb, hands, feet, up, right side and left side. Dristhi purifies and stabilizes the functioning of the mind.”