The story of Noah focuses on the word promise. Sin continued on the earth from the time of Adam to Noah. The earth became so wicked that God decided to judge the earth and its people for their sin. But in that judgment there was also hope, because God planned to save some and establish a covenant with them. God is a God of promise, and he always fulfills his promises.
When Noah came out of the ark, after the flood subsided, his first act was to offer a sacrifice to God (Gen. 8:20-21). This sacrifice was pleasing to God, it changed God’s attitude toward mankind by turning away his anger through the atonement for sins. God promised to never again curse the ground or strike down every creature.
Jesus has done the same for us. He has turned away God’s wrath toward us for our sins by his perfect and complete sacrifice. The judgment and sacrifice that happened in the story of Noah points forward to an even greater promise and promised one. Jesus is the promised one, and all the promises of God are yes in him (2 Cor. 1:20). Just as the rainbow reminds us of one promise, so the manger and the cross remind us of another.