It comes about from machine learning algorithms that could pick up on patterns from a small number of examples. Few shot means only a handful of examples to recognize something. One shot means only a single example. And zero shot means no examples. Of course, you have to indicate what you want somehow, but in the case of an LLM that's the prompt. Once LLMs were trained for instruction following, you didn't have to give any examples, you could just give a prompt describing what you want, and that was a zero-shot.
