Savasana is a continuation of the meditation. The purpose here is to relax -- to surrender control of body and breath -- without losing the awareness cultivated through the asana or pranayama practice. This is much more difficult than it sounds.
BKS Iyengar has written of this pose that "the stresses of modern life are a strain on the nerves, for which Savasana is the best antidote." Savasana not only removes fatigue from the body but, when practiced with intention, quiets the mind and strengthens the practitioner's ability to enter a relaxed, meditative state. This, in turn, heightens one's ability to function in an environment of total assault on the senses, something that many of us face on a daily basis whether we realize it or not. (Forget battle or natural disasters, have you been to a mall lately?)
I find that consistent practice of Savasana for at least a few minutes a day adds significant depth and perspective to my practice, as a whole. While the idea of death as relief may be an uncomfortable subject for some, it is important to remember that Savasana is the reward, the moment of transition. While it is tempting to skip the final posture and get on with your day after practice, to forgo rest or allow the mind to wander is to relinquish the fruits of your labor. So why not stay a while and enjoy?