Wiktionary
n. (context politics English) A group of countries whose leaders have been persuaded by another to take up a specific task, usually in the context of an invasion or war.
Wikipedia
The clause coalition of the willing generally refers to a group of allied countries in a military intervention, especially the United States and its allies, in the Iraq War. It has existed in the political science/international relations literature at least since UN peacekeeping operations began to run into complications in 1993-94, and alternatives began to be considered. One early use was by President Bill Clinton in June 1994 in relation to possible operations against North Korea, at the height of the 1994 stand-off with that country over nuclear weapons.
It has also been applied to the Australian-led INTERFET operation in East Timor.