The "Good News" or "the Gospel" is how Bible translators have translated the Greek word euangelion into English. This Gospel or Good News, as I've heard a teacher recently explain it is simply that God is both holy and loving. Because He is holy He must punish sin. But because He is loving he sent His Son Jesus Christ to live, then die on a cross and rise again. On the cross Christ satisfied the holiness of God (by taking the punishment for sin) and He also satisfied the love of God (by providing a way for people to be saved).
When we believe in Christ (trusting Him for the forgiveness for our sins) we will be saved and accepted by God. This faith, or belief, is a belief that Christ "lived the life we should have lived and died the death that we should have died."
Quite simply, the message of the Gospel "is that you are more wicked and sinful than you ever dared believe but you are more loved and accepted than you ever dared hope."
So, "though we are wicked, we are absolutely loved and completely accepted through Jesus Christ."
These words that I've quoted on the Gospel were explained by Tim Keller, Pastor at Redeemer Presbyterian Church in New York City.
I heard some additional comments on the Gospel by Rev. Keller this week in a video called "What is Gospel-Centered Ministry?" In his lecture he explains what ministry shaped by the Gospel looks like.
Here is the link: http://www.thegospelcoalition.org/video/what-is-gospel-centered-ministry
I really enjoyed his comments, I hope you will too.