无缘无故 is a four-character idiom (成语) meaning 'without any reason or cause'. The literal components — 无 'without', 缘 'reason/predestined connection', 故 'cause' — reinforce the idea that something happens entirely groundlessly. You can use it to describe an action, event, or emotion that has no apparent explanation, often with a slightly negative or puzzled tone. It functions as an adverbial phrase and is not separable.