Mercy is the act of not administering justice when that justice is punitive. Because of our sinfulness, we deserve death and eternal separation from God (Rom. 6:23; Isaiah 59:2), but God provided an atonement for sin and through it shows us mercy. That is, He does not deliver to the Christian the natural consequence of his sin which is damnation. That is why Jesus became sin on our behalf (2 Cor. 5:21) and bore the punishment due to us (Isaiah 53:4-5). It was to deliver us from damnation. (Compare with justice and grace).
God saved us according to His mercy (Titus 3:5), and we can practice mercy as a gift (Rom. 12:8). "Let us therefore draw near with confidence to the throne of grace, that we may receive mercy and may find grace to help in time of need." (Heb. 4:16).