When practicing Yoga asana you have a choice of giving priority to the periphery of the body (arms & legs) or the core of the body – specifically the back (or to be even more specific – the spine). The spine is a central channel for the nervous system – it connects the brain to the rest of the body and it’s various organs and systems. According to Yoga philosphy – the spine correlates to the central Sushumna Nadi which is at the heart of energetic system that is you and therefor the focus of many Yoga practices. Also, the lower back is an area highly prone to injury (most of the back-problems you hear about are in the lower back) because it is vulnerable and often neglected and weak.
Try bending forward. If, like many people, your flexibility is limited, then you may find it difficult to reach the floor. If your legs are straight – then the stretch in your legs is at the expense of stretching your back – your are giving priority to a peripheral stretch. If you want to change that and provide your back & spine with more range of movement and stretch – then bend your knees.
You can also experience this explicitly in seated forward bends. Many people have a hard time just sitting straight, not to mention actually bending forward. Again, bend your knees and discover a whole new range of movement.
When I began practicing Yoga I could not sit on the floor with my legs straight and back erect. I practiced for years with my legs (and arms!!) straight which led to frustration and no change or improvement in my practice. Then when I began studying with my teacher, I was given this simple and remarkable piece of advice, in the spirit of viniyoga, which changed my practice (and me) forever.
As a Yoga teacher, I have experienced that the greatest obstacle students face in embracing and applying this idea is a stubborn ego. People have been told for too long (since elementary school gym class) by too many people (play-Yoga teachers included) that this is they way to do it. People are pursuing an external image of how they want to stretch rather then practicing with respect to their present condition. Bend your knees.