It was instituted by His Holiness Pope Pius XI, of Blessed Memory, in 1925 by his Encyclical Letter, Quas Primas.
Quas Primas was a development of ideas going back to the Church Fathers, but concretely presented earlier by Leo XIII, and Pope Pius himself. Pope Leo had said in Annum Sacrum,
His empire extends not only over Catholic nations and those who, having been duly washed in the waters of holy baptism, belong of right to the Church, although erroneous opinions keep them astray, or dissent from her teaching cuts them off from her care; it comprises also all those who are deprived of the Christian faith, so that the whole human race is most truly under the power of Jesus Christ.
And Pope Pius had said in his Ubi arcano Dei consilio,
...(A)s long as individuals and states refused to submit to the rule of our Savior, there would be no really hopeful prospect of a lasting peace among nations.
A short comparison of the Rites:
The Collect from the Traditional Roman Rite:
Almighty and everlasting God, who in thy beloved Son, the King of the whole world, hast willed to restore all things: mercifully grant that all the families of nations, now kept apart by the wound of sin, may be brought under the sweet yoke of his rule.Who with thee liveth and reigneth, in the unity of the Holy Spirit, one God, world without end.
And for comparison, the Collect for the Feast from the Missal of Pope Paul VI:
Almighty ever-living God, whose will is to restore all things in your beloved Son, the King of the universe, grant, we pray, that the whole creation, set free from slavery, may render your majesty service and ceaselessly proclaim your praise. Through our Lord Jesus Christ, your Son, who lives and reigns with you in the unity of the Holy Spirit, one God, for ever and ever.
A pretty stark difference, eh? From all the nations of the world brought under the sweet yoke of Christ's rule to all of creation rendering service and proclaiming God's praise. The last time I checked, all of creation, except Man and the fallen angels, did all of that as essential to their nature.
Of course, this was completely in line with Annibale Bugnini's plans to protestantise the Liturgy.
“We must strip from our Catholic prayers and from the Catholic liturgy everything which can be the shadow of a stumbling block for our separated brethren that is for the Protestants.”
“The liturgical reform is a major conquest of the Catholic Church, and it has ecumenical dimensions, since the other Churches and Christian denominations see in it not only something to be admired in itself, but equally as a sign of further progress to come”
With one exception the readings have been changed, as well. In the Traditional Rite, the Epistle is Col 1:12 - 20, and the Gospel is John 18:33 - 37. The Gospel from John survives in Year B in the three year cycle, Year A being Matt 25:31-46, and Year C, Luke 23:35-43
And, by placing it on the last Sunday in October, it was deliberately placed close to 'Reformation Day', kept by many protestant churches on the same Sunday to celebrate the heresiarch Luther's rebellion against Christ's Holy Catholic Church. Therefore, moving it was done to placate the heretics.
The doctrine of the Feast is expressed very well in this prayer from Fr Stedman's Jesus+Mary+Joseph Novena Manual:
HAIL, CHRIST, OUR KING
MOST SWEET JESUS! Come near to us, Thy children. Receive from our hands that crown which those who are but dust of earth, try to seize from Thee. Enter now in triumph among us, Thy fervent Lawmakers may break the tables of Thy Law, but whilst they lose their thrones and are forgotten, we, Thy subjects, will continue to salute Thee « Hail, Christ, our King!
They have said that Thy GOSPEL is out-of-date, that it hinders progress, and must no longer be considered. They who say this soon disappear into obscurity and are forgotten; whilst we, who adore Thee, continue to salute Thee « Hail, Christ, our King!
The proud, the worldly « those who possess unlawful riches « those who thirst for riches, honors and pleasures alone « declaring Thy moral law to be for past ages « will be hurled against the Rock of Calvary and Thy Church and falling, will be reduced to dust, and sink into oblivion, « whilst we, Thy followers, continue to salute Thee « Hail, Christ, our King!
Those who seek the dawn of a material civilization, divorced from God, will surely die, poisoned by their own false doctrine, deserted and cursed by their own children « whilst we, who would console Thee, will continue to salute Thee« Hail, Christ, our King!
Yes, hail to Thee, O Christ, our King! Put to flight Lucifer, the fallen angel of darkness, from our homes, schools and society « force him and his agents into Hell « chain him there everlastingly « whilst we, Thy friends, continue to salute Thee« Hail, Christ, our King!
Stedman, Fr. Joseph F.. Jesus, Mary, Joseph Novena Manual: The New Revised (Kindle Locations 935-952). Confraternity of the Precious Blood. Kindle Edition.
An excellent explanation of the ideas and doctrines of the Feast of Christ the King may be read in Mr Michael Davies', The Reign of Christ the King. This booklet is a transcript of the keynote speech at the Catholic Voice International Conference in Chicago in the early 1990s. I was also a speaker at the conference on the subject of Christ the King and Monarchism, so I got to hear Mr Davies deliver his speech, after having been privileged to have dinner with him the night before.
And for those who do not have access to the prayers and hymns of the Traditional Office of Christ the King, here is a 'Little Office' I compiled some years ago, based on the example of the approved Little Offices, such as the Immaculate Conception, St Joseph, and the Holy Angels. (pdf file available here.)
Here is a traditional prayer to Christ the King, which is really an Oath of Allegiance to His Kingly Powers:
O CHRIST, JESUS, I acknowledge Thee as Universal King.
For Thee, all creatures have been made. Do Thou exercise
over me all the rights that Thou hast.
Renewing my Baptismal Vows, I renounce Satan,
with all his works and pomps, and I promise to live as a
good Catholic: Especially, do I pledge myself, by all
the means in my power, to bring about the triumph of the
rights of God and of Thy Church.
Divine Heart of Jesus, I offer Thee all my poor actions to obtain that all hearts may recognize Thy Sacred Royalty and that thus the Reign of Thy Peace may be established throughout the entire world.
Christ The King From "The Saint Andrew Daily Missal" (1953):
That Christ is King over all creation is the theme of the whole Mass and Office of the feast. The Mass begins with the magnificent Apocalyptic vision of the Lamb of God, sacrificed but henceforth glorified forever, acclaimed by the innumerable host of Angels and Saints (Introit). By its position on the last Sunday of October, towards the end of the Liturgical year and just before All Saints, the feast of Christ the King comes as the climax of our celebration of all Christ's mysteries and a kind of earthly anticipation of his everlasting reign over the elect in the glory of heaven. It sums up the Christian message that by his Death and Resurrection Christ has conquered sin and death and reigns in the glory of his victory among the elect who are its fruit. Christ is the creative Word; He is the Man-God, seated at the right hand of the Father; He is our Saviour; these are His three titles to kingship.