What are some examples of grave reasons? Or emergency situations?
This is a very good question, and it is unfortunate that the issue has never been resolved. It was 53 years ago when Pope Pius XII granted that NFP could be permitted within certain limited constraints. He mentioned "grave reasons of a medical, economic, social or eugenic nature." But during the past half century we have had Vatican II and Humanae Vitae and then "The Theology of the Body," and no one has ever presented a more definitive explanation of what these terms are supposed to mean.
BTW, besides the grave reasons, there are a couple of other essential conditions for practicing NFP that are usually omitted from these discussions:
1. Both partners must agree. It cannot be unilateral. This is because the marriage right is "permanent, continuous and uninterrupted." That means that one marriage partner can never deny the marriage right to the other partner without committing a grave injustice unless there is some sufficient reason why it is inopportune to fulfill the marriage obligation at this time, but it must be fulfilled as soon as it becomes opportune.
2. Both partners must be able to fulfill the conditions without the temptation of falling into sin. If continence, even periodic continence, were a source of temptation towards masturbations, adultery, etc. for either partner, then NFP could not be attempted. Even if there were proportionally grave reasons, no reason can ever justify mortal sin. Better to die without mortal sin, if that be the alternative, rather than commit mortal sin even to save a life.