Picture a weekly notice from party managers landing on a British MP's desk. Every item on it is : one line for 'come if you can', two for 'we would like you there', three for 'you are coming and you are voting our way'. The number of lines is the amount of pressure, and three is the top of the scale. Everything this phrase does in English grows out of that one picture of a line drawn three times under an instruction.
可以想成英國議員桌上每週收到的一張通知單。上面每件事都畫了底線：一條線是「有空就來」，兩條線是「希望你到」，三條線是「你一定要到，而且要照黨的意思投」。底線的數量就是壓力的大小，三條是最高的一級。這個片語在英文裡做的每件事，都可以從「在指示底下畫了三次線」這個畫面長出來。
From the word’s history
The name is literal: party managers send British MPs a weekly document called 'the whip', and the most important votes on it are underlined three times.
這個名字是照字面來的：英國黨團每週發給議員的文件就叫 the whip，上面最重要的表決會被畫上三條底線。
Wiktionary, "three-line whip"
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