Good news (gospel) was used during the Greco-Roman time by messengers when they returned from the battle field to inform the king, emperor or ruler of the victory. The phrase is used purposely in the Bible to tell of the greatest victory of the greatest battle in history. In the Bible's battle story, good news is proclaimed to the world of God's victory over the greatest enemies to God - humanity (sin) and Satan.
Even likened to a cosmic court of law, God judged the world guilty of sin and separation while he also sentenced mankind to hell. The good news is that God loves the world and promised a substitute to take the place of anyone sincerely trusting him. Therefore, the substitute would take upon the punishment, which would reconcile the sinner to God in an eternal relationship that ends in heaven, the eternal home of God. Evil will exists until God ends it forever, but he wants humanity to eternally live with him forever. His patience allows people the opportunity to believe in him. If he were to kill off evil, then he must kill off the world -- the world that he loves.
In the Bible
The good news is that God the Son Jesus came into the world to be the substitute. He's the only perfect sacrifice to take upon the sin, separation and sentence of mankind. He did so through dying by the hands of sinners on the cross during the Roman Empire in the city and county of Jerusalem, Israel. Three days later, Jesus resurrects from death to life, which proved to the world that he's trustworthy and more powerful than death. Paul writes in the Bible's New Testament about the gospel of Jesus:
Now I would remind you, brothers, of the gospel I preached to you, which you received, in which you stand, and by which you are being saved, if you hold fast to the word I preached to you—unless you believed in vain. For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, that he was buried, that he was raised on the third day in accordance with the Scriptures, and that he appeared to Cephas, then to the twelve.
Then he appeared to more than five hundred brothers at one time, most of whom are still alive, though some have fallen asleep. Then he appeared to James, then to all the apostles. Last of all, as to one untimely born, he appeared also to me. For I am the least of the apostles, unworthy to be called an apostle, because I persecuted the church of God. But by the grace of God I am what I am, and his grace toward me was not in vain. On the contrary, I worked harder than any of them, though it was not I, but the grace of God that is with me. Whether then it was I or they, so we preach and so you believed. (1 Corinthians 15:1–11 ESV)
In Our Life
God inspires the world through truth and love to believe him. Paul writes again in the Bible's New Testament:
If you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and is justified, and with the mouth one confesses and is saved. (Romans 10:9–10 ESV)
When one believes him, they become a follower of him, which are also known as Christians, people of God or the church. Our hearts act like good soil -- humble and receptive to his truth -- that bears fruit of loving him and others. God commands the church to love one another, which includes gathering locally together as part of a life of worship -- poured out for his purposes and glory. God works through his church to love the world and reveal the good news of Christ Jesus' life, death and resurrection for them to be with God forever. Christians are a transformed people.