I'll put it as plainly as I possibly can. The word "yoga" means to yoke or unite. The practice draws the body and mind together, reversing the outward sensory flow most of us operate in, while establishing internal awareness and consciousness in order to experience accurate knowledge about ourselves and surroundings.
Why is this necessary? Because most of us are focused on doing instead being, existing instead of living, leaving us empty and unfulfilled.
My definition may sound esoteric; a loose depiction of a very physical practice. But what the western world fails to realize is that yoga isn't really physical at all. Yoga postures are a small fragment of the practice as a whole.
The History of Yoga
Patanjali, the said father of yoga, created the 8 Limbs of Yoga as a way to restore awareness of our oneness with God. The physical yoga practice is only the 3rd limb, reaffirming that the yoga journey is a diverse one.
Most of us start with the physical practice, but there are others who start with meditation or pranayama (breath work), first. Yoga finds each of us in a unique time and space, but the practice as a whole would not be complete without the representation of each of the 8 limbs.
Why Should I Practice Yoga?
Do you want to know yourself, intimately? Are you interested in learning why you are the way that you are and what it means? If so, that's partially your soul, pining for the opportunity to express itself, it's greater passion.
I know I'm not the only one unsettled with my external purpose and internal make up; frustrated with my inability to perceive my infinite position with God, and inundated with emotional loose ends. If you can identify with any of the observations I just stated, yoga might be a good practice for you to take up, my friend!
The practice itself isn't going to solve your problems or suspend your questions. Rather, it will dissolve dependence on external senses and establish internal awareness so that problems are no longer perceived as such, and a pool of answers lie in wait at the center of your heart as soon as your gaze turns inward.
Basically, yoga is going to help you discover you. That's a pretty awesome reason to give the practice a shot. If you don't believe me, at least try it out and prove me wrong.