A Christian is someone who not only believes what Jesus said about himself, but who also trusts in his sacrifice on the cross to pay his/her debt of sin. Every human being has broken God's moral law (Romans 3:10-12, 23), and the penalty is death, alienation from God, and hell (Romans 2:8; Matthew 10:28). God is just in punishing sin because every sin is a rejection of his good and loving rule over his creation (Romans 1:18). But God is also gracious and merciful, choosing to bear himself the punishment that we deserved through Jesus' death on the cross (Romans 3:23-26; Colossians 2:13-14). Jesus, who was entirely without sin, endured not only the extreme physical torture of Roman crucifixion, but the full weight of God's own wrath against sin (Isaiah 53:4-6). God showed that the sacrifice was sufficient and the debt was satisfied by raising Jesus from the dead (1 Corinthians 15:17; Romans 8:34). Christians believe this to be true and stake their eternal hope on it.
Even though Jesus calls us to obedience and generosity in response to his love, we don't trust our good works to gain us favor from God (Romans 3:20, 28). We know that a just judge punishes for the crime committed, no matter how much other good a person may also have done. Instead we trust the perfect life and death of Christ in our place (2 Corinthians 5:21), and we ask him to help us live lives that express our love and gratitude for his grace, and to share this love and grace with others.