The Jewish and/or Roman authorities were uncomfortable with revolutionary movements and ideas. He was publicly executed by the Romans in a rather gruesome way. Crucifixion killed slowly by pressing the weight of a hanging body against the lungs. Eventually the chest muscles no longer have the strength to draw breath and the victim suffocates surrounded by fresh air.
It had been around in Judaism for quite a while
The gruesome death of Jesus shocked his followers. The Messiah was supposed to battle the Romans and win. It seems likely that the majority of his followers felt his death resolved the question of whether he was the Messiah. For some of those closest to Jesus there had to be some other explanation. Death could not be the end of what they were so sure was the start of something radically new. If there was some meaning behind the horrible death of Jesus, it was very confusing.
The sources we have report that the confusion was resolved by eye-witness testimony of the empty tomb and sightings of Jesus. It is possible to accept this proposition on faith and be done with it. Scholars today offer longer accounts of how the followers of Jesus came to find meaning in his death as necessary but not permanent. The two major answers are that Jesus suffered and died in order to transfer the sin of others to himself, and in order to defeat death.
3.4.1. Transfer sins
First a little background is necessary on the concept of sin at the time of Jesus. Economic metaphors were used for sin and suffering. When one does wrong one “owes” God, the way one might “owe” a quarter to a swear jar after using impolite language. 
Thus, sin is a debt. However, one cannot pay the debt with money, but only suffering, blood, or death. The idea is that we all have balance sheets in the sky. The more we sin, the more we owe suffering.
One idea was that the blood of an animal could substitute for the blood of the sinner. Thus one could sacrifice an animal to God to pay off the balance sheet. This idea is actually a tad complex, and not all Jews would have accepted this way of putting it. For some New Testament writers, though, Jesus was the perfect sacrifice who replaces the need for ordinary animal sacrifice. Thus John gives Jesus the title, “ Lamb of God who takes away the sins of the world.” An ordinary son of a sheep might take away some sins, but the sacrifice of the son of God is much more effective. Personally, I don’t think this idea was dominant.
The idea which I do think is dominant does not have to do with animal sacrifice, but it is related in the sense of substitution. The idea was that the total balance sheet had to amount to zero, but that one could pay other people’s debts . Thus, Jesus had no sin-debts, but paid the ultimate suffering-price. With those extra credits he could pay off the debts of his friends and followers. The theological term for suffering on behalf of others is vicarious suffering .
As previously discussed, the followers of Jesus came to believe that he fulfilled the scriptures . That meant they could turn to scriptures for clues as to the meaning of his suffering and death. In the book of Isaiah (combined with Psalms and other sources) they found an explanation of the suffering of a person who did not deserve to suffer, but voluntarily suffered on behalf of others. This figure is called the suffering servant . The original audience understood the suffering servant as a metaphor for the Israelites who went into exile in Babylon. They appeared to have been defeated and to suffer the fate of horrible sinners. Contrary to appearances, they were actually advancing God’s plan. Their suffering gave a fresh start (zero balance-sheet) to others, and gave God an opportunity to reveal Godself to all nations. The followers of Jesus interpreted this passage as providing the key to the meaning behind the death of Jesus and the greater good that would come out of it.