What does it mean to have zero population growth?

Zero Population Growth means that as many people are born as will die in a given year. This is difficult to achieve, because every improvement in health care and medical processes will both extend life span of the elderly who were about to die AND will increase the health of mothers and newborn babies, both of which will disturb the ZPG balance. So it's a probability process, and since none of this stuff is really under anyone's control, it's hard to manage.