Quas Primas - encyclical of Pope Pius XI on the Feast of Christ the King - promulgated on Dec 11, 1925 - click to read

Holy Trinity painting is by Raphael

Paragraph 15 in the encyclical letter of Pope Pius XI gives us description of Christ's Kingdom:

(Christ) kingdom is spiritual and is concerned with spiritual things. That this is so the (above) quotations from Scripture amply prove, and Christ by his own action confirms it. On many occasions, when the Jews and even the Apostles wrongly supposed that the Messiah would restore the liberties and the kingdom of Israel, he repelled and denied such a suggestion. When the populace thronged around him in admiration and would have acclaimed him King, he shrank from the honor and sought safety in flight. Before the Roman magistrate he declared that his kingdom was not of this world. The gospels present this kingdom as one which men prepare to enter by penance, and cannot actually enter except by faith and by baptism, which, though an external rite, signifies and produces an interior regeneration. This kingdom is opposed to none other than to that of Satan and to the power of darkness. It demands of its subjects a spirit of detachment from riches and earthly things, and a spirit of gentleness. They must hunger and thirst after justice, and more than this, they must deny themselves and carry the cross.

More reading on the Kingship of Christ in this world from Christian Order