He is a King Who stoops low to identify Himself with the lowly. He shepherds them to Eternal Life, meeting their needs, including their greatest need of salvation.
And as the narrative in the Gospel passage makes clear, He expects the same of us who participate in His Kingdom.
I sometimes puzzled over how Christ could be present in the needy of the world. Then I realized that He is present in all people because His image, the Divine image, is in all people. If someone has unmet physical needs, doing something to help those people restores them to the dignity of God's image.
So when all the nations are gathered before the great King at the End of Time in the great judgment, we will recognize that Jesus Christ is a Great King, and He directs our lives by commanding us to care for those in need, as a way to advance His Kingdom.
Pope Pius XI established this Feast in 1925 at a time when the manifestations of worldliness meant there was a need to uphold a different image of Kingship. Jesus Christ has rightly earned the title King of the Universe because He stooped to the level of humanity, died, and then rose to New Life. We share in the dying and rising to enter His Kingdom as we fulfill the mission He has given us on Earth.