Gospel means "good news." The good news is: you are more sinful and flawed than you ever dared believe yet you can be more accepted and loved than you ever dared hope at the same time because Jesus Christ lived and died in your place. As the apostle Paul said, "God made him who had no sin to be sin for us, so that in him we might become the righteousness of God."
That is the simple formulation of the gospel. More thoroughly we could say that the whole Bible is the gospel. It is a book about the God who rescues people from their moral and spiritual rebellion against him. The teaching of the Bible, the gospel, can be summarized under four heads: God, Man, Jesus Christ, and Our Response.
Firstly, the gospel teaches that God is our creator. Thus he has the right to rule and command us as he does in his law. God is also holy, that is, he is absolutely pure morally, and he hates and punishes rebellion on the part of his creatures. He is more holy than anyone would ever imagine.
Secondly, the gospel teaches us about human beings. We are creatures made by God and for God. We were originally created to live in relationship with God and we were morally pure. But because our first parents rebelled against God (just as we also all have done), human beings are now cut off from relationship with God and are subject to his condemnation. We are more sinful than we ever dared believe.
Thirdly, the gospel teaches us what Jesus Christ has done for sinners like us. He became a man and lived a life of perfect obedience to God's law, and then died as a sacrifice in our place under the judgment of God. He was raised from the dead and now reigns in heaven. The condemnation that he suffered takes away the necessity that we suffer judgment for our own sins- "God made him who had no sin to be sin for us." The righteous life he lived is credited to us, not because we are actually righteous, but because of God's mercy and grace- "in him we might become the righteousness of God."
Fourthly, the gospel teaches us how to respond to the good news. We turn away from our rebellion and put our trust in Jesus Christ. Despairing of our own worthiness to stand before God, we believe the promise that those who trust in Jesus Christ will be forgiven and declared righteous. Those who put their faith in Jesus Christ are accepted as loved sons and daughters of God, and God sends his Spirit to live in them.
Martin Luther said that a sinner trying to believe the gospel was like a drunk man trying to ride a horse; he will always be falling off on one side or the other. The two errors that the sides of the horse represent are 1) legalism or moralism and 2) pragmatism or relativism or antinomianism.
Moralism is the view that a person is made acceptable to God through his own attainments. Moralists are usually very religious, and often very conservative in their religion. Legalism tends to stress truth without grace. Moralists are usually very rules oriented, and depending on their success in keeping the rules they will be either arrogantly self-righteous or depressed and morose. If they go to Jesus for forgiveness, it is just to ask him to fill in the gaps they have left in their own religious performance. For the moralist, the cross is not the only basis for acceptance by God, but is an adjunct to our performance.
Pragmatists are often irreligious, or prefer more liberal religion. They tend to stress grace over truth, assuming everyone is accepted by God and that we each have to decide what we think is true for us. Often relativists will talk about God's love, but since they do not see them selves as deeply sinful people, God's love for them costs him nothing. For them the cross is not the necessary condition of our acceptance by God.
The gospel holds out to us a whole new system of approach to God. It rejects our attempts to justify ourselves before God, to be our own saviors and lords. It rejects both our pragmatic presumption and our religious attempts to earn our way into God's favor. It destroys the perception that Christianity is just an invitation to become more religious. The gospel will not let us think Jesus is just a coach to help us get stronger where we are weak. To be a Christian is to turn from self-justification of all sorts and to rely exclusively on Jesus' record for a relationship with God.
Christians and non-Christians both stumble over the two counterfeits of the gospel. Many Churches are deeply moralistic or deeply relativistic. Christians who understand the gospel very clearly still look like the drunk man on the horse, as the desire to justify ourselves and trust in our own performance continually reappears.
The gospel tells the pragmatist that he is more flawed and sinful than he ever dared believe. The gospel tells the moralist that he is more loved and accepted than he ever dared hope.