The Catechism in Questions & Answers

135. What is meant by the “kingdom of God”?

The “kingdom of God” is not a national territory, nor is it a political sphere of dominion. Rather the “kingdom of God” means that God is present and rules among mankind.
In the person of Jesus Christ, the Son of God, the “kingdom of God” has come to all people (cf. Luke 17: 21). Jesus Christ is the ruler, He creates justice, He grants grace, He turns to the poor and needy, and He brings salvation.
“Kingdom of God” also has a future significance—it will begin with the “marriage of the Lamb” and endure eternally in the new creation (cf. Revelation 21: 1- 3).

Marriage of the Lamb: see Questions 566. et seq. Kingdom of peace: see Questions 575. et seq. New creation: see Question 581. “Your kingdom come”: see Question 635.

The gospel of Matthew uses the term “kingdom of God” synonymously with “kingdom of heaven”.
The term “kingdom of God” is a designation for the presence and regency of God among mankind. It was already possible to experience this in the time of Jesus. Today too the “kingdom of God” is present and perceptible in the church of Christ, in which Jesus Christ is at work—in other words, in word and sacrament. On the other hand, we also await the future “kingdom of God”.
This kingdom will be manifested in the “marriage of the Lamb”, in the kingdom of peace, and in the new creation.