How many examples you give the model before asking it to do something. Zero-shot means you simply describe the task. Few-shot means you show it two or three worked examples first. Showing examples is often the fastest way to improve results, especially when you want a specific format, and it usually beats trying to describe that format in words.
Technical view
This is in-context learning: the model adapts its behaviour from examples in the prompt without any parameter updates. It was one of the notable emergent properties of scale. Example selection and ordering both affect results measurably, and gains typically plateau after a handful of examples. Instruction-tuned models have narrowed the gap between zero-shot and few-shot performance considerably compared with early base models.
Related
Part of AI Terminology Index, section: Controlling and Extending Behaviour at Run Time.