In Chapter 21, the fox asserts that if he is tamed, life will matter to him. It is important to remember that the fox is using a different definition of tame than we normally would. The fox defines it as "to establish ties," something that is "too often neglected." The fox sees taming as a bond, the same sort of bond that takes place between owner and pet. We on the other hand, would define taming as turning something into a state of submissiveness, or the act of controlling (Collins English Dictionary). Therefore, if you miss seeing the fox describing the act of taming as the act of creating a bond, like the bond between owner and pet, which can be viewed as love, than you'll miss why he at first hesitates at the thought of being tamed and then asks the prince to tame him.
If the fox were tamed, he would love the prince, which would break the fox's heart if the prince went away because, of course, love hurts. Yet the fox embraces the idea of being tamed because, as he states, his life currently has no meaning. His life is monotonous. Presently, all he does is hunt chickens and run from hunters. Presently, things that are useless to him have no meaning in his life, just as the wheat fields have no meaning because he does not eat bread. But if he were to establish a bond with the prince, he would then be able to view the wheat field as beautiful because the prince's golden hair is the same color as the wheat field. Therefore, looking at the beautiful wheat would remind him of the prince and bring him joy, creating in him a new-found love for not just the prince, but the wheat, as we see in his line, "I shall love to listen to the wind in the wheat."
Therefore, if the prince were to tame the fox, or to create a bond, the fox would suddenly need the prince in his life, to create joy in his life, to break the monotony, because the fox would then love the prince. In loving the prince, the prince would then become special to the fox rather than continue to be just another little boy, which is what the fox means in his lines:
But if you tame me, then we shall need each other. To me, you will be unique in all the world. To you, I shall be unique in all the world...(Ch. 21)
Hence, we see that to tame as the fox understands it is to create a bond, or love, and loving a person makes you need that person in your life.