Prompt
A prompt is a request for additional information given by a moderator to a player whose answer to a question is partially correct but ambiguous. In this scenario, the player is said to have been prompted because the answer they gave was promptable - alternatively, they may say they were prompted on their answer. Receiving a prompt allows a player an opportunity to give an additional answer.
A player may receive multiple successive prompts. It is possible for a player to intentionally aim to be repeatedly prompted to stall or to attempt to gain additional information about an answer.
The set of answers which warrant a prompt is enumerated in the answerline alongside the acceptable answers. Under strict readings of the rules, no answers other than those written down should be prompted on; moderators will occasionally use their discretion to determine that an answer should be prompted on or accepted, but this is to be avoided.
Examples
The most common reason for a prompt is that a player has answered with a superset of the correct answer.
ANSWER: the second Punic War"; prompt on the Punic Wars]
ANSWER: polar bears [or Ursus maritimus; prompt on bears]
Answers which are insufficiently specific to uniquely identify a single person are typically prompted on - for instance, if multiple people in a field share a surname.
Philosophy
Prompts are a recognition that questions are not typically written precisely enough to allow only a single correct answer (or set of answers). The need for some prompts could be removed by careful editing, but in general it is not possible to remove ambiguity from every clue without making questions transparent or otherwise impacting their playability.