Christians believe that Jesus came to the earth to fulfill Old Testament prophesy, to save sinners and the lost, to defeat the devil and to cast away sin. God wrapped Himself in human flesh as Jesus to provide eternal salvation to the world.
The Old Testament speaks of the Lord's coming, and Jesus fulfills that prophesy. In Matthew 5:17, He Himself says He has come to fulfill. In Romans 5:18, it is written that He came as promised to Israel's fathers.
The goal of God becoming flesh was to save sinners and provide a way to salvation for the lost. Matthew 18:11 and Luke 19:10 both say He came to seek and save those that were, and still are, lost.
After Jesus died on the cross, He battled the devil for the keys to the kingdom of Heaven. Matthew 16:19 and Revelation 1:18 explain His delivery of the keys and the defeat of evil. After His resurrection, He gave those keys to Peter and explained how Peter should build His church.
The blood that Jesus shed was the only way to wash away the sins of mankind. As He died, His blood provided atonement for the sins of people then, and people today. The Bible references this blood sacrifice in John, Ephesians, Hebrews, 1 Peter, 1 John and Revelation.
Other Biblical reasons for Jesus coming to earth include service, abolishing Old Testament sacrificial law, giving life more abundantly to those who follow Him and preaching. He also brought fire and baptism, provided judgement, was a living sacrifice and served an example to mankind of how to live a holy, righteous life.