I notice that a regular flow of visitors to this blog arrive here by googling the question, "What are principalities and powers?" Up until now they have been disappointed by what they have found, at least as far as the answer to that question is concerned. Seekers from the four corners of the worldwide web, here is the answer (or the beginnings of it).
There are two different uses of the terms, the one is primary and political, whereas the other is secondary, or derived, and spiritual.
In Ephesians 1:20-21, it is above every authority, starting with political ones, that Jesus is exalted. "He raised Him from the dead and seated Him at His right hand in the heavenly places, far above all principality and power and might and dominion, and every name that is named, not only in this age but also in that which is to come" (NKJV).
He is "seated," indicating sovereign rule. That seat of authority is at the right hand of God the Father. So his rule is a divine government that does not merely closely rival earthly government, but is "far above" it. His power does not rise and later fall like the kingdoms of men, but is everlasting.
Because Jesus reigns with utterly unassailable power from heaven over every principality and power on earth, Paul can tell the followers of Jesus to obey those earthly principalities and powers. He tells Titus to teach the Christians in his church, "to be subject to principalities and powers, to obey, to be ready for every good work, to speak evil of no one, to be peaceable, gentle, showing all humility to all men" (Titus 3:1) Because Christ is in control from heaven and is able work all our sufferings on earth for our good, we can obey even pagan governments as though they were Christ himself, unless they command us to sin.
In his commentary on the Bible, John Charles Ellicott (1819-1905, Bishop of Gloucester), tells us this:
The Greek words translated "principalities and powers" are better rendered here by "rulers and authorities," as the word "principalites" is used occasionally in the English version for an "order of angels." The terms include all constituted governors and officials, Roman and otherwise, in the island [Crete] (comment on Titus 3:1).
George Eldon Ladd says this in A Theology of the New Testament, rev. ed. (Eerdmans, 1993) in his section on spiritual powers:
A prominent element in Paul's thinking about the nature of the old age is the conviction that it is in the grip of evil supernatural powers. Paul conceives of both good and evil spirits. Angels are viewed as spiritual beings engaged in the service of God. ... The archenemy of God, however, is an evil spirit who is sometimes called the devil (Eph. 4:27; 6:11; 1 Tim. 3:7), but usually Satan. ... Satan's main objective is to frustrate the redemptive purposes of God....He argues that Paul used this symbolic language, "to assert that all evil powers, whatever they may be, whether personal or impersonal, have been brought into subordination by the death and exaltation of Christ and will eventually be destroyed through his messianic reign" (p. 442).
Paul refers not only to good and bad angels, to Satan and to demons; he uses another group of words to designate ranks of angelic spirits. The terminology is as follows: [rules, authorities, powers, thrones, lordships, etc.]. That this terminology designates spiritual beings is quite clear from Eph. 6:11ff., where the believer's struggle is against the devil and against principalities, authorities, world rulers of this present darkness, spiritual hosts of wickedness. Usually they are conceived as being evil and opposing the Kingdom of God. Sometimes, however, these spiritual powers are not cast in an evil light but are represented as created beings who apparently exist to serve the divine glory (Col. 1:16). Christ is the head of all such rule and authority (Col. 2:10); the divine purpose will display to these principalities and powers in the heavenly places the manifold wisdom of God through the church (Eph. 3:10) (pp. 440-441).
I contend, however, that Paul can use terms such as principalities, powers, thrones and dominions to refer metaphorically to supernatural powers like angels and demons only because what he is saying is primarily true of those earthly powers to which the terms most literally refer.
So, in the New Testament use of the terms, sometimes principalities and powers are earthly political authorities, sometimes they are angelic beings, and sometimes they are specifically fallen angelic beings, viz., demons, depending on the context.
Ladd recommends that we read G. H. C. MacGregor, "Principalities and Powers," in New Testament Studies 1 (1954); H. Schlier, Principalities and Powers in the New Testament (1961); and G. B. Caird, Principalities and Powers (1956).