The "argument by design" holds that the world is full of complex, highly organized things that could not have emerged but for the acts of an intelligent designer. Darwin's theory of natural selection dealt a death blow to this argument in the realm of biology. His theory showed how complexity can ratchet up in small increments as randomly generated beneficial traits get preserved while deleterious ones get discarded.
Natural selection works in a finite world. The earth is 4 1/2 billion years old -- very old, to be sure, but not infinitely old. Likewise, the universe is about 14 billion years. But what if the world were infinite? Perhaps it is. The multiverse theory suggests there could be an infinite number of universes, each isolated from all others but unfolding according to its own laws and contingencies.
Infinity overturns our intuitions about probability. We feel that something whose probability is infinitessimal will not and cannot happen. This idea, in fact, is implied by the Second Law of Thermodynamics, which states that a closed system must tend toward entropy. That is, an isolated system must move from an ordered (improbable) state to a disordered (more probable state.) Open a door between a hot room and a cold room. The fast-moving air molecules of the hot room will start mixing with the slow-moving molecules of the cold room until the temperature of the two rooms equalizes. But couldn't this process be reversed, with all the fast-moving molecules going to one room while the slow ones go to the other? Yes, but the probability of randomly moving molecules spontaneously sorting themselves in this way is so small as to boggle the mind. Nevertheless, given an infinite number of trials, an improbable event -- no matter how improbable -- becomes likely, or even necessary. Multiply an indefinitely small probability by an indefinitely large number and you get a probability approaching one -- that is, certainty.
Thus, in an infinite world, any event that can happen, no matter how improbably, must happen.
So, in an infinite world no intelligent designer is needed to create highly improbable complex systems; they can -- and must -- arise spontaneously. This is true even outside the realm of living things, where natural selection holds sway.