Death is the separation of the soul from the body. We have no way of knowing precisely when that occurs so we look for combination of medical signs.
The Church herself does not come up with the criteria for death. The way these things generally develop is that medical science comes up with various criteria for death that are then evaluated by the Church and accepted or rejected.
The combination of signs that modern medicine uses to officially declare that someone has died has not been controversial and has long been accepted by the Church. The most recent criteria that has been somewhat controversial that has been accepted by the Church is that “brain death” is an acceptable criteria for moral certainty that a person has died.