How does this work? Different Christian groups understand the atonement in different ways, many of which overlap. One way, the 'ransom' approach, draws on Mark 10:45, where Jesus says he gives his life as a "ransom for many." The 'Satisfaction' or 'Vicarious Atonement' approach says that Jesus' blood is payment to God for human sins. Since the penalty for sin is death, someone had to pay it; Jesus paid the debt in place of humanity, giving humans eternal life. This ties in with a view of the atonement as the fulfillment of divine justice. Though many liberal Christians find this view's transactional language and emphasis on justice harsh, the 'vicarious atonement' view is held as truth among evangelcial Protestants and other conservative Christians. A more liberal view maintains that Jesus' death was an example to his followers, not a form of blood sacrifice.
Most Christians of any denomination would say Jesus' death demonstrates God's love for humankind.