The Gospel
God sent His Son to earth not in a man, but as a man. He was born of a human mother of the lineage of David (Romans 1:3). But His father was God the Father. Jesus Christ was both fully man and fully God. His mission was to redeem those whom the Father had given to Him (John 6:37; Matthew 20:28). As a man, Jesus, in obedience to the Father, kept every aspect of the Law of God inviolable. He was sinless. Jesus Christ was not only righteous because He is God, He earned His righteousness as a man in His obedience to the Law. Then He offered Himself as a sacrifice to atone once and for all for the sins of all who believe in Him. Jesus was a perfect man, and only the blood of a sinless man could atone for the sins of the unrighteous. What Jesus did was take upon Himself our sins, and then the Father's wrath was poured out on Him instead of us. It's like this: We owed God a debt we could not pay (the sins of men against an infinitely holy God are therefore infinitely sinful), and Jesus paid our fine (only an infinitely holy God--Jesus Christ--could pay our infinite debt against Him). After paying our fine in His life's blood, He rose from the dead, defeating death and proving that the Father was pleased with His atoning work. Now, as our risen Savior, He imputes the righteousness He earned to our account.
I heard an interesting metaphor a while ago. If we each had a book of all the sins we've ever committed, it would be a very thick book with every page filled to capacity. If Jesus also had such a book, every page would be blank. What Jesus did for us was to trade books. He took our sin-filled book and as a result, was punished by the full extent of God's wrath. But then He gave us His pure, blank book in return. God sees us with this new book and gives us eternal life. Our sins have been punished in Christ, but we are made righteous through the righteousness Christ gave to us. Isn’t that wonderful? What a beautiful Savior!
We have had our sins paid for and are made righteous in God's eyes all because of Jesus Christ. Our response to this gloriously good news is to repent of our sins and place our faith in Jesus Christ alone for our salvation. That is the gospel.