This is a crucial topic. The way of body awareness can boost your growth like few others. I will now try to make a case for it, but really you just have to make it a priority, a constant focus, and trust me, you will see the fruits, in abundance, I've seen them, and keep seeing more every day that passes.
Someone once said that the body is the temple of the soul...
 
Here is are various aspects of what I define as body-awareness, and some of its benefits (not in any particular order):
Being aware of the force of gravity pulling you down, rooting you, gives you stability and security; it grounds you. Open your body, do not close up - it will reflect the way you face life situations: are you willing to drop resistance and denial, and accept and deal with your current circumstances? Notice that your body, even in psychologically and emotionally challenging situation is always fine. Get it. Unless you get physically injured, your body is mostly doing just fine. If you can realize this, it will show you great freedom. While exercising, be aware of your bodily sensations: especially of your joints and breath. It will ensure that you do not hurt yourself, after repetitive unconscious movements. RELAX. Let the energy, the emotions, be. Feel into your chest and belly. Stay with whatever arises. It is a way to clean your suppressed emotions; in fact, once allowed and listened to, they will gradually bubble up, and release. Be conscious of the breath, and breath fully. Progressively inhale expanding: diaphragm > lower ribs > upper chest. And then, exhale, emptying the lungs in the opposite order. It is optimal to massage with your breath your internal organs, and to allow the oxygen to clean all the waste. Relax your shoulders while typing or working at the desk (easier said than done!!). It will reduce your stress, and as a consequence you will be less drawn to waste hours on the internet. Flow like water, be gentle and yet firm with your movements: the body reflects the mind, and viceversa. Feel into pain. Being deeply aware of unpleasant physical sensations, such as tension and pain, will greatly reduce both the pain itself, and also the mental suffering which is created and attached to the unpleasant sensation. Focusing on bodily sensations will greatly reduce your futile thoughts and monkey-mind. It will anchor you in the now, so you can witness them easily. "Until the cup will be empty". Paradoxically, at a certain point you will develop a certain detachment from the body, distancing yourself. You will slowly realize that all that you know about this body are the sensations, and in the same way you witness your thoughts and realize they are not you, you will witness bodily sensations and slowly realize that you are not limited to them. Awareness of your body and emotions while eating will be enough to tell you when you are overeating (in case that's your thing) Being conscious of your body in relationships to other people bodies, while interacting and speaking, will allow you to have more effective interactions, and more impactful speech. Also, discrepancies between what you are saying and your posture, are probably a signal that you are not being fully authentic.  
Sources:
My own experience, as a human being, as a dancer, a yoga practitioner, and a life-long learner. Zen body-being - Peter Ralston Emotional clearing - John Ruskan The science of breath - Yogi Ramacharaka @Leo Gura you might find this useful
Ask me if you have any questions. I hope you enjoyed