A 'Close Shave' means a narrow escape from danger or an unpleasant situation. For example: 'That was a close shave — the car nearly hit him.' The phrase originates from the literal sense of a blade passing very close to the skin without cutting. While 'hair's breadth' and 'by the skin of one's teeth' also convey closeness, the direct meaning of 'close shave' is specifically a narrow escape.