The complex interplay of random mutations and non-random natural selection is what makes biological evolution possible.
In Chance and Necessity (1971), Jacques Monod explained this elegantly:
Drawn out of the realm of pure chance, the accident enters into that of necessity, of the most implacable certainties. For natural selection operates at the macroscopic level, the level of organisms.
Even today a good many distinguished minds seem unable to accept or even to understand that from a source of noise natural selection alone and unaided could have drawn all the music of the biosphere. In effect natural selection operates upon the products of chance and can feed nowhere else; but it operates in a domain of very demanding conditions, and from this domain chance is barred. It is not to chance but to these conditions that evolution owes its generally progressive course, its successive conquests, and the impression it gives of a smooth and steady unfolding.
This basic notion is something the creationists and all the other similar-minded evolution-deniers can't seem to grasp.