The store is holding a clearance sale as they're going out of business.

going out of business 是一个固定短语，由动词短语 go out of 和名词 business 组成。 go out of 表示"离开、退出"某种状态或活动。 business 在这里指"商业经营、生意"。 going out of business 整体意思是"停止营业、倒闭"，指企业即将结束经营。