We are reminded that this feast was instituted in 1925 by Pope Pius XI in Quas Primas. The pontiff specifically chose the last Sunday of October with an intended purpose.
28. Therefore by Our Apostolic Authority We institute the Feast of the Kingship of Our Lord Jesus Christ to be observed yearly throughout the whole world on the last Sunday of the month of October -- the Sunday, that is, which immediately precedes the Feast of All Saints. We further ordain that the dedication of mankind to the Sacred Heart of Jesus, which Our predecessor of saintly memory, Pope Pius X, commanded to be renewed yearly, be made annually on that day. This year, however, We desire that it be observed on the thirty-first day of the month on which day We Ourselves shall celebrate pontifically in honor of the kingship of Christ, and shall command that the same dedication be performed in Our presence. It seems to Us that We cannot in a more fitting manner close this Holy Year, nor better signify Our gratitude and that of the whole of the Catholic world to Christ the immortal King of ages, for the blessings showered upon Us, upon the Church, and upon the Catholic world during this holy period.
29. It is not necessary, Venerable Brethren, that We should explain to you at any length why We have decreed that this feast of the Kingship of Christ should be observed in addition to those other feasts in which his kingly dignity is already signified and celebrated. It will suffhice to remark that although in all the feasts of our Lord the material object of worship is Christ, nevertheless their formal object is something quite distinct from his royal title and dignity. We have commanded its observance on a Sunday in order that not only the clergy may perform their duty by saying Mass and reciting the Office, but that the laity too, free from their daily tasks, may in a spirit of holy joy give ample testimony of their obedience and subjection to Christ. The last Sunday of October seemed the most convenient of all for this purpose, because it is at the end of the liturgical year, and thus the feast of the Kingship of Christ sets the crowning glory upon the mysteries of the life of Christ already commemorated during the year, and, before celebrating the triumph of all the Saints, we proclaim and extol the glory of him who triumphs in all the Saints and in all the Elect. Make it your duty and your task, Venerable Brethren, to see that sermons are preached to the people in every parish to teach them the meaning and the importance of this feast, that they may so order their lives as to be worthy of faithful and obedient subjects of the Divine King.
The conclusion seems obvious. The culmination of the crowning glory of Christ's earthly life and mission is proclaimed and commemorated in this feast. Before the triumph of the saints on Nov 1, we celebrate Christ's.
The pontiff encourages all of us to make this day special and to order our lives to being Our Lord's faithful and obedient subjects.
Furthermore, take the opportunity to pray to the Sacred Heart.