Much of your action in martial arts is accomplished with your palms and fists. Blocking, striking, adapting and overcoming is first trained through your hands. In the beginning one learns to strike and block. All martial arts adhere to this ideal– offense and defense; protect and destroy. There are 8 primary methods for wielding in Taiji (in reality there are a plethora of different energies in internal martial arts but Taiji concentrates on these 8 in the beginning). These are Roll-back, ward-off, press, push, bump, elbow, rend/split, and pluck (again within these energies are subset of other jins/energies, many things are interconnected but details can be better interpreted with proper in-class discussion ;). Now the 4 primary skills of roll-back, ward-off, press and push should be practiced thoroughly to gain true skill. Yang Banhou (elder son of Yang Luchuan, founder of Yang Tai Chi) professed this in his book, relegating the other 4 energies to the inability to truly wield the primary 4 in all situations [1].
The greatness of internal martial arts and especially utilized in Tai Chi is the idea of Hua Jing, transformational energy. If one is able to stick, then adhere, then connect, and finally follow an opponent you have begun to grasp the idea of accepting energy. You will be able to know your opponents will and transform with it so that he may not grasp yours. From there one must learn to deliver this energy back through neutralizing, leading, controlling, and issuing. Thus you can attain the idea of moving 1000 pound with 4 piddly ounces! This is most easily accomplished with your hands (but a true master can wield from any part of his body ;).
There are more esoteric concepts as well. If Qi is abundant and you have filled your 4 extremities, the issuing of energy will be stronger and more vibrant. Your body will be more alive, agile, and have a stronger ability for both transference and wielding. These skills appear miraculous but really are honed ability through years of daily dedicated solo and partner practice, proper lifestyle, and thorough discovery of ones true nature.
[1] Yang, Banhou. Explaining Taiji Principles. Section 23. translated by Paul Brennan. https://brennantranslation.wordpress.com/2013/09/14/explaining-taiji-principles-taiji-fa-shuo/.