What is the Gospel? The word "gospel" itself simply means "good news". What is the good news? Well, as with many scenarios there is good news and there is bad news. So let's start with the bad news first.
According to Romans 3:23, every person has sinned. Sin means to "miss the mark". Like an archer aiming his arrow at the target and missing it. Our target is perfect obedience to God's law and we have all missed it.
The other bad news is that our sin causes death (Romans 6:23a). This is not only physical death (every human being dies), but it's also a spiritual death. We are separated eternally from God. There is a form of separation while alive on earth, and once we die there is an eternal separation in Hell.
The good news comes in the second half of Romans 6:23: the gift of God is eternal life! You do not have to be eternally separated from God. How does this happen?
We see in Romans 5:8 that God showed his love to us by sending Jesus to die in our place so we don't have to suffer an eternal punishment for our sin.
Jesus' death was a substitution for us so that we can be saved from God's wrath (Romans 5:9)
How can we know that we are saved from God's wrath? Romans 10:9-10 tells us that if you believe in your heart that Jesus is the Lord and that God raised Him from the dead, you will be saved.
The really great news is that when we accept Jesus' payment for our sin we have peace with God (Romans 5:1) and we are no longer condemned to Hell (Romans 8:1).