Although the Asana's (poses) of Hatha Yoga are not a system to increase flexibility (it is a system to create balance), flexibility is a consequence of asana and thus one of its main attractions. Many people look to do yoga to improve their flexibility. The theory being, the greater the range of movement at a joint, the less rigid the joint becomes. This leads to freedom of movement and increased health. When a muscle stays partially contracted (or short), an abnormal state of prolonged shortening called contracture develops. Contracture not only shortens the muscle, it makes the muscles less supple, less strong and unable to absorb the shock and stress of various types of movement. The most appropriate remedy for this is to stretch and relax the muscles. A relaxed muscle is defined as the "cessation of muscular tension".
Ultimately, optimum flexibility, which is simply proper range of motion at a joint increases efficiency of movement which is the key to physical health.
As an analogy, the great B.K.S Iyengar (1979) explained:
"To the Yogi, his body is the prime instrument of attainment. If his vehicle breaks down, the traveler cannot go far. If the body is broken by ill-health, the aspirant can achieve little. When the body is sick or the nervous system is affected, the mind becomes restless or dull and inert and concentration or meditation becomes impossible".
Whatever the goal is for the practising "yogi", an additional side benefit of asana will be the benefit of flexibility. With that being said, lets look at some science behind flexibility.
What are Muscle Spindles?