The gospel is most simply the good news about God's plan to rescue sinners and redeem a fallen world through the means of His own Son, Jesus Christ.
Let's break that statement down:
He is the Creator of all things, including us, and therefore we owe Him our ultimate allegiance. He is also completely loving and holy, and therefore must judge sin.
Although we were created in God's image, we have defiled and marred that image by our sin. Our sin is more than what we do - it's who we are. God's rightful judgment rests on each one of us as a result.
The second person of the Trinity, who is both fully God and fully man, perfectly obeyed and fulfilled God's righteous requirements without any sin. Yet, bearing the sins of the world he was crucified, experienced God's wrath, died, and was buried. He rose on the morning of the third day, overcoming sin and death and vindicating that the penalty he paid was satisfactory.
God commands all men and women everywhere to repent of (turn from) their sin and place their trust in Jesus Christ alone to receive eternal life. The Christian life is marked by worship and obedience to God's revelation as each believer is conformed into his image.