Immortale Dei is an 1885 encyclical of Pope Leo XIII on Church-State relations, and specifically on the topic of civil allegiance, which is defined as a duty of loyalty and obedience which a person owes to the State of which he is a citizen.
The word allegiance is a derivative of liege, free, and historically it signifies the service which a free man owed to his liege lord. In the matter in hand its meaning is wider, it is used to signify the duty which a citizen owes to the state of which he is a subject.
Read more about Immortale Dei: The Catholic Encyclopaedia View, Origin of The State, The State Not Secularist, The Church As Divine Society, Relation Between Both Powers, The Church's Temporal Jurisdiction