The maps between the kernels and the maps between the cokernels are induced in a natural manner given the exactness of the rows; the important statement of the lemma is that a "connecting homomorphism" d exists which completes the exact sequence.
The maps between the kernels are induced in a natural manner. The maps between the cokernels are induced in a natural manner. This natural manner is given the exactness of the rows. The important statement of the lemma is that a "connecting homomorphism". D exists which completes the exact sequence homomorphism.