This is a programed cell death but it is important to understand that this cell death can be part of normal life. When the fetus is developing cells between it's fingers go through apoptosis in order to create the fingers. On the other hand there are cases where the apoptosis is a pathological phenomenon. this happens when cells are in stress.
Another thing to think about is that there are cases where the body uses apoptosis to defend itself, for instance against cancer. When cancer cells start to form the body tries to stop them by causing apoptosis in the cells that are cancerous. A similar thing happens when viruses attack the body. Apoptosis is induced in the cells around the place the virus entered in order to stop it from spreading.
These examples should give you an idea of how important and basic this process is in our daily bodily functions.