Depends. It is common to use the term blue baby to describe an infant with a congenital heart defect that prevents the addition of sufficient oxygen to keep baby pink. Some might use the term to describe any infant requiring respiratory support at birth. In my experience, the are all blue as they are delivered as they need/get less o2 in the womb, but pink up the first minute or so when breathing normally.
Mgt. They may have been referring to a medical condition called cyanosis. A decrease in blood oxygen level can be a result of many cardio-pulmonary conditions. Some babies at birth during the transition to room air may be cyanotic. If there is any current change in the baby's skin color, please see your PCP right away.