It is important because it speaks to Jesus' nature. As Christians we believe that while He was God, He gave up the independent use of his innate God abilities. Thus, we believe that when He healed people, it was the Holy Spirit doing the healing... etc. etc. You get my point, the conversation can be confusing very quickly, but you get the basic idea.
We believe that Jesus was killed because he was being faithful to His Father's will. Or he was being himself. Jesus was teaching a new way, and then while living this new way, he was killed in the most shameful way possible. This death is the utter rejection of Jesus by the Jews. They wanted to make a statement about what they thought about Jesus...and they picked the cross.
As Christians we believe that God has the final say in our lives. Thus we believe that when God raised Jesus from the grave he was vindicating the life that Jesus lived, "This is my Son, with whom I am well pleased." This means that the way God has ordained for us to live is the life that Jesus lived. That the way the world finds detestable, is really the way that we are to live. We are to subvert the ways of the world around us, because we find our honor in ways the world finds shame.