It is a famous analogy which has been used by both sides in the evolution debate: If you give one or more monkeys typewriters and an infinite amount of time, supposedly they will eventually produce the works of William Shakespeare.
The necessary rationale for that is of course infinity: in an infinite amount of time, randomness will (it is believed) produce every possible circumstance. But since evolution doesn’t have an infinite amount of time, and is not completely random, those who object that this is a poor argument for evolution seem to be right.
But that is not an argument against evolution, but merely a problem with the analogy.
If we want to make a realistic analogy to evolution, one can have computers (or monkeys, if one really prefers) generating random sequences of letters. Like DNA, there should only be four letters used in the “alphabet” of this “language.” In the “language” in question, all words are three letters long. And every word means something.
That would be a better analogy to evolution. DNA involves four different molecules, arranged in “words” three molecules long. Every combination means something, even if only “Ignore me.” And we know that letters get changed through mutations – that much is observable and well-documented.
There is a lesson in this: choose your analogies wisely. Monkeys with typewriters with only four keys, and a language with no spaces, and in which every combination of letters means something, illustrates the way evolution works. The poor analogy of monkeys using ordinary typewriters to eventually accidentally type Shakespeare only serves to make it seem implausible. A good analogy, on the other hand, should help even skeptics understand how evolution works and why it makes sense.