Answer: Typically as a woman's pregnancy nears the 9th month, the cervix (which is the opening to the uterus) begins to soften, open and thin out (something that we call "ripening") in anticipation of delivery. Sometimes, however, this doesn't happen and the cervix remains as it was in the beginning of the pregnancy.
If you are past your due date and your practitioner has checked your cervix and noted that it is still closed, there are a few other details to consider. If this is your first pregnancy, the cervix may remain closed until labor begins even if the cervix has started to thin out (efface) or soften. In most women, the cervix will begin to ripen at some point--for some that is at 36 weeks and for some that is 42 weeks.
If, on the other hand, your cervix is still closed and otherwise not ripe (not thinned out or soft) and you are one to two weeks past your due date, there is a chance that you may need to be induced. There are some risks to continuing a pregnancy past a certain point and this is an important conversation to have with your practitioner so that you and your partner are well-educated on the risks and benefits of labor induction.