mainly UK informal(通常指女子)年龄太大而找不到对象的 If someone, usually a woman, is on the shelf, she is not married and is considered too old for anyone to want to marry her.
In those days, if you hadn't married by the time you were 30, you were definitely on the shelf. 在那个时代,如果你到30岁还未结婚,那就肯定嫁不出去了。