The gospel literally translates as good news. The gospel is the good news that Jesus is miraculously born, lived a sinless life, died the most humiliating sacrificial death, rose from the grave, and will one day return to make all things right. Jesus does all of this to pay for our sin and give us everlasting life. Christians believe this to be true and respond to the work of God in repentance and faith.
Here is another way to look at the gospel:
God created all things and it was good.
God also created man. God gave man dominion on earth with one command. Man rebelled against God as Adam and Eve ate of the fruit that God instructed them not to eat. (Genesis 3) Satan deceived man and since this original sin all of man kind has been sinners from the womb.
God in the moment of the original sin promised a solution to sin. This solution is Jesus. Jesus is completely righteous. Jesus is fully man and fully God. Being fully righteous Jesus was able to serve as an acceptable sacrifice for our sins. In our sin we are dead. (Ephesians 2:4) There is nothing that we can do that can save us from our sin. All we have to look forward to is the wrath of God. In Jesus we have hope. Because Jesus was righteous and freely gave his life (John 10:17-18) on the cross for our sins, believers rejoice that we are made new in Christ. We are no longer seen as sinners, but as righteous in the eyes of God. (Romans 5:20-21)
The bible describes those who believe that Jesus died on the cross for their sins and have responded to this belief with repentance of sin are Christians. Christians are new creations in Christ. As new Christians we are to live our lives in obedience to his word, in repentance for our sin, bearing fruit in the spirit, all for the glory of God.