Nismat is a great site for information about stretching and flexibility. Check out
physical therapy.
Muscles can get tight and shorten and then have limited prospects for growth.
If your trying to increase muscle size, you need to exercise a muscle over the entire length of contraction, not just at the peak of contraction.
Having a flexible muscle enables you to do this because you can contract the full distance. If the muscle is tight, it can't go very far.
If a muscle cannot be extended very far, the muscle may get stronger in the contracted position, but strength building that might have occurred in the extended position cannot take place. Some strength gains, and thus some size gains, are missed.
This also negatively impacts the shape of a muscle too. If not all parts of the muscle are stressed in the same weigh, the shape as the muscle grows will be a bit distorted.
Also, if a muscle has been injured in the past, it can actually have tough areas called lesions where muscle function is actually a bit impaired. An accumulation of these lesions causes a muscle to shorten. Stretching a muscle can, over time, break up these lesions!
That's my theory anyway. And stretching has a strong tradition in so many cultures and sports. If see the same answer to many different questions, you know there's something important there.