In my experience, most Christians would answer this question by mentioning either 1.) the death and resurrection of Jesus “for us”, or 2.) the “formula” of salvation/justification (i.e. apart from works, by grace, through faith, with redemption in the afterlife as the endgame), or perhaps both if they are more theologically sensitive to important nuances. Both are indeed aspects of the good news of the gospel, but when viewed in isolation like this, both answers forget the larger framework of the New Testament witness. What is the essential content of the good news that Jesus proclaims in the Gospels? That the kingdom of God has come! What is the core focus of Paul’s proclamation as an apostolic missionary? That the crucified and risen Jesus who saves us is now Lord over all (that is, the King in whom the kingdom has finally come)! How is it, then, that we are so comfortable proclaiming a gospel that seems to have no necessary, organic connections to the kingdom of God and the lordship of Jesus Christ over the world?
If we are faithful to the NT witness, we will ultimately distinguish between the central content of the gospel (the return of God’s saving rule over the world through a faithful, image-bearing human being, Jesus, through whom God has dethroned the tryannical powers of sin, Satan and death), and the means by which this good news was accomplished and made possible (the life, death, resurrection and exaltation of Jesus) and why that is good news “for us” (because this is a King–in fantastic contrast not only to the Caesars and Hitlers of history, but also finally to the previous reign of Satan through sin and death–who loves us and uses every ounce of his authority and power to serve our good, and who relates to us by grace and not by what we deserve). If we maintained these distinctions in our communication of the gospel, we would learn to read the Bible as a unified, comprehensive story so much more compelling and powerful than our reduced, “me-centered” versions of Christianity.
Here are a few other writers who preserve these crucial distinctions when it comes to the gospel, and who see the kingdom of God as logically central to the gospel:
“The Kingdom of God is conceived as coming in the events of the life, death, and resurrection of Jesus, and to proclaim these facts, in their proper setting, is to preach the Gospel of the Kingdom of God.” (C. H. Dodd, The Apostolic Preaching and Its Developments, p. 24)
“[Gospel] becomes the terminus technicus for the missionary message of the coming of God’s rule through the mission, cross, and resurrection of Jesus.” (Peter Stuhlmacher, “The Theme: The Gospel and the Gospels,” in The Gospel and the Gospels, ed. Peter Stuhlmacher, p. 21)
“The coming of God’s righteous rule took place in the crucifixion and resurrection of Jesus.” (Carl E. Braaten, That All May Believe: A Theology of the Gospel and the Mission of the Church, p. 176)
“Both the singular noun ‘gospel’ and the cognate verb were employed to describe the early Christian preaching of the coming of God’s rule as evidenced in the coming of Jesus, his death and resurrection.” (P. T. O’Brien, Gospel and Mission in the Writings of Paul: An Exegetical and Theological Analysis, p. 80)
“The ‘gospel’ is the message about the promised return of God’s reign, now appearing through the person of Jesus from Nazareth.” (Jonathan T. Pennington, Reading the Gospels Wisely: A Narrative and Theological Introduction, p. 11)