Genesis is full of well known stories and Noah's Ark is one of the most well known. The effect of the fall has taken root and sprung a stronghold in humanity. It was so established in humanity that it came to the point where God makes this observation: "The Lord observed the extent of human wickedness on the earth, and he saw that everything they though or imagined was consistently and totally evil" (Genesis 6:5). They were only capable of thinking evil, never any good. God was so removed from them that there was no goodness left. The only one who had some righteousness was Noah.
The sin of humanity is so evil to God that He cannot be in it's presence and so decides to restart creation. Noah is the only one who is righteous and so he is the one God chooses to restart creation with. Noah shows that he is truly righteous because he "did everything exactly as God had commanded him" (Genesis 6:22). The ridiculousness of the request is often shown in movies based on the stories. Noah, or a character based upon Noah, is commanded to build an ark and everyone laughs at him like he is crazy only to be regretting not listening earlier when the rain comes.
Building an ark to carry a pair of every animal while a worldwide flood wipes out those not on it sounds ridiculous to us today. We often think that because of the lack of science in ancient times that they could more easily believe things like this actually happened. In reality this concept was most likely just as ridiculous to Noah and those around him. But Noah had faith that God could do such a thing and would do such a thing if He said so and so He was careful to carry out His exact instructions.
Once the flood recedes and Noah, his family, and the animals emerge from the ark the first think Noah does is thank God for His mercy. God had every right to extinguish the human race but yet He had mercy on Noah and his family. Although God knows that humanity is still lost in sin He promises not to flood the earth again, "I will never again curse the ground because of the human race, even though everything they think of imagine is bent towards evil from childhood. I will never again destroy all living things" (Genesis 8:21). God had a plan to save humanity instead of condemning them.