The Principalities — Archai in Greek, the plural of the word translated 'beginning' or 'first principle' — are the first order of the third and lowest angelic sphere, the sphere most directly engaged with creation and humanity. Their distinctive role is the angelic governance of nations, peoples, and the institutions of human authority.
The biblical foundation for this is Deuteronomy 32:8 in the Septuagint reading preserved at Qumran: 'When the Most High divided the nations, when he separated the sons of Adam, he set the bounds of the peoples according to the number of the sons of God' — that is, the number of the angelic beings of the divine council. Each nation, in this reading, was given an angelic prince. The clearest narrative confirmation comes in Daniel 10, where the angel speaking to Daniel describes a celestial conflict with 'the prince of the kingdom of Persia,' a being who could withstand the angel for twenty-one days until Michael came to help. The 'prince of Greece' is named in the same passage. These princes are the Principalities.
The order is named explicitly in Paul's lists of the powers Christ has created and now rules — Romans 8:38, Colossians 1:16, Ephesians 1:21. But Paul also speaks of the fallen members of the same order in Ephesians 6:12, where the wrestling of the saints is 'against principalities, against powers, against the rulers of the darkness of this world.' Some of the Principalities, like Persia's prince in Daniel, are no longer ministers of the Most High; they have set themselves against him.
Patristic theology — particularly in Origen, Eusebius, and later Pseudo-Dionysius — develops the doctrine of the angels of the nations as part of the cosmic context for the gospel. The proclamation of Christ to the nations is, in this reading, the breaking of the Principalities' usurped authority. Christ is the true Prince of all peoples; the gospel is the announcement that the older arrangement is now ended. Ephesians 3:10 says the Church itself is the means by which the wisdom of God is now declared to these very principalities and powers in the heavenly places.