Leniency is a noun that refers to the lessening of a punishment or chore. Your father's leniency, for example, resulted in you not having to paint the entire house like your mother wanted. Instead you just had to paint the garage.
Leniency also refers to a person's sense of mercy or tolerance. A governor's leniency could be demonstrated when he pardons the prisoners on death row. Leniency comes from the adjective lenient, which describes someone who is tolerant or permissive. There are times when too much leniency can backfire, however. If your teacher shows leniency to the loud students who won't sit still and refuses to punish them, the rest of your class won't learn much.