To be fired or dismissed (from a job); an informal idiom emphasizing losing one's position.
うちの部署は業績が悪くて、この前、課長の首が飛んだ。
Our department's performance was poor, and the section chief was fired the other day.
ミスが続けば君の首が飛ぶかもしれないから、気をつけて仕事をしなさい。
If mistakes keep happening, you might get fired, so be careful with your work.
リストラで何人か首が飛ぶと噂が出ている。
There are rumors that a few people will be let go in the restructuring.