In these times there were strict rules prohibiting unmarried people of different sexes from speaking directly to each other. If a man was interested in a woman, he would hand her a mirror. If she looked at herself in the mirror and handed it back face up, it meant that she was interested in him also. If she turned the face of the mirror down and handed it back, it meant that she was not interested in him. Many people attach a sexual connotation to this phrase, but the true meaning has nothing to do with sex.
Many items come with adjusting bolts or nuts to allow it to be fitted.
The current meaning of this phrase is that a decision has been made and the future is set and can not be changed. This phrase is often misstated as the dice are cast or tossed. Actually this phrase has nothing to do with dice. In industry, a die is used to shape a series of identical parts. This phrase is commonly used to indicate that a person desires sex.