Let's start with a quote from a favorite author of mine: Ravi Zacharias
Jesus Christ did not come to make bad people good, but to make dead people alive.
The central tenet of Christianity is that man is a fallen, sinful creature, and thus spiritually dead. Christ sacrificed himself on the cross to pay the price for that sin, and thus made his believers spiritually alive again. This is the free gift of Christ: accept that death as a sacrifice for your own sins. John 3:16 encapsulates this
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
Christians commonly call this giving your life to Christ. It is commonly symbolized by most Christian denominations through baptism, the symbolic death of the old, sinful self, and the start of a new life in Christ.
What Christians gain in return is something called the Holy Spirit (referred to by Jesus as The Advocate in this version). John 15:26-27
“When the Advocate comes, whom I will send to you from the Father—the Spirit of truth who goes out from the Father—he will testify about me. And you also must testify, for you have been with me from the beginning."
The Holy Spirit is what aids Christians in their walk as new creations. In addition, Christians are expected to remember Christ's sacrifice and act differently. Galatians 2:20 (emphasis mine)
I have been crucified with Christ and I no longer live, but Christ lives in me. The life I now live in the body, I live by faith in the Son of God, who loved me and gave himself for me.
And Jesus himself in Luke 9:23-26
Then he said to them all: “Whoever wants to be my disciple must deny themselves and take up their cross daily and follow me. For whoever wants to save their life will lose it, but whoever loses their life for me will save it. What good is it for someone to gain the whole world, and yet lose or forfeit their very self? Whoever is ashamed of me and my words, the Son of Man will be ashamed of them when he comes in his glory and in the glory of the Father and of the holy angels.
The concept here is clear: Christians are expected to live differently than they did before because Christ now lives within them.