When a pregnant woman is past her due date, the doctor will often induce labor, meaning he'll give her drugs that will start the contractions that will result in the birth of the baby. ("Labor" is the word used to describe the time between when the mother's water breaks and the baby is actually born.)
In the first panel of the cartoon, the bird is relating a childbirth story, telling the others how the doctors had to induce labor. However, in the last panel, the Boss is using the other meaning of labor, as in "work." He is wishing there was a drug or method that he could use to make his staff more efficient.