The precise theological significance of the death of Jesus on the cross is rooted in Jewish tradition.
First, the significance of the event is rooted in the Jewish traditions of Passover in which a perfect, unspotted lamb was sacrificed. The blood of the lamb, smeared on the doorposts of the houses of the Jews, caused God, who was killing the first born sons of Egyptians as punishment for their impiety, to pass over the sons of the Jews. Thus, in some ways, the lamb is a substitute sacrifice. A ram is sacrificed rather than the son Isaac in the Old Testament story of Abraham and Isaac; the Passover story echoes this typology.
Jesus Christ is described in the New Testament as the "lamb of God who taketh away the sins of the world" and serves as a substitutionary sacrifice for Original Sin. the significance of the cross is thus that Jesus died for human sin and in order to save human souls.