오지랖 is an outdated word. Here's a dictionary definition.
오지랖 - 웃옷이나 윗도리에 입는 겉옷의 앞자락 = The front (opening) part of a coat or other upper body garment.
It survives in these idioms.
오지랖이 넓다 = Have wide coat flaps => Go around getting involved in others' matters (in good or bad sense).
오지랖을 떨다 = Stick one's nose in others' matters (mostly negative).
In modern Korean, we use 앞(front) or 앞부분 (front part) instead of 오지랖.