breadth是“宽度”，a hair 's breadth即一根头发的宽度，就是千钧一发或毫厘之差的意思。

【例句】
The seal is air-tight—there's not a hair's breadth between the door and the frame.
封口是密不透风的，门和门框之间没有毫厘之差。

After wandering around the forest for an hour thinking we were lost, it turned out that we were only a hair's breadth away from our campsite.
在森林里转悠了一个小时，以为我们迷路了，结果发现我们离营地只有极短的距离。