When a player or team captain gives a partially-correct answer to a question which is not specific or exact enough to cover the entire answer that the question is looking for, the moderator may prompt the player for a more specific answer, giving the player a few more seconds to specify further.
For example, there might be a question with the answer line:
ANSWER: polar bears [or Ursus maritimus; prompt on "bears"]
If a player gave the word "bears" as their answer, the moderator could prompt them by saying some phrase along the lines of "I'll prompt you," "More specific, please," "I need more information," or even just saying the word "Prompt." At that point, the player has a few more seconds to refine their answer to the correct one; adding no new information counts as an incorrect answer.
A prompt line is the part of a question's answer line which specifies some partial answers that the moderator may prompt on.
Prescriptively, a moderator prompts the player upon hearing the less-specific answer. Descriptively, quizbowlers often use the word "prompt" as though the answer itself is the thing being prompted (hypothetical example: "The answer line said 'polar bears', so I prompted 'bears'"), though this makes less etymological sense.