"And surely, the blood of your lives I will demand; from every animal will I demand it; and from man, even from every man's brother, will I demand the life of man. One who spills a man's blood - by man his blood shall be spilled - for in God's image He made man." (9:5-6)
There are two parts to this statement. In the first God says He will hold people and animals accountable if they kill people. In the second, people are commanded to execute murderers, and an explanation is given for why.
What is the meaning of the explanation? The obvious meaning is that since humans are created in God's image, it is especially serious to kill people, and thus we must be especially sure to punish murder.
I think there is another possibility. In the first half of the statement, it seems that God carries out the punishment for murder. In the second half, people carry out the punishment. From where do people derive the authority to carry out punishments, which were previously the sole responsibility of God?
It appears that since people reflect the Divine, they are given the authority to execute punishments along with God. In the original Hebrew, the phrase "in God's image" is "betzelem elokim". The name of God used here is traditionally held to correspond to the Divine attribute of justice. Indeed this name, "Elokim", in other contexts means "judges". Thus "in God's image" could be loosely translated as "with the capability to judge". Because we reflect God, we therefore have the authority and ability to carry out punishments.
Hashem smelled the sweet smell [of sacrifices], and Hashem resolved: "I will never again curse the earth because of man, since the inclination of man is evil from his youth, and I will never again kill all life as I did." (8:21)
What caused God to make this decision? R' Amnon Bazak points out that the phrase "since the inclination of man is evil from his youth" actually explains why God might want to have another flood, not why in the end God resolves not to. Therefore, the reason for the resolution cannot be found in the resolution's text.
Therefore, we must look to the resolution's context for help. God's resolution comes immediately after Noach offers sacrifices and seems to be a reaction to them. But both our theology and our sensibilities object to the possibility of God's being "bribed" by physical enticements like the smell of burning meat. And in any case, people (Kayin and Hevel and likely others) offered sacrifices before the flood, yet the flood occurred nonetheless. So what about Noach's sacrifices in particular induced God to forswear the possibility of a future flood?
Let us look at Noach and the context in which he offered the sacrifices. The Torah calls Noach righteous, but how righteous was he? Rashi famously observes that Noach walked with God (Breishit 6:9), while Avraham walked before God (17:1). Noach's service of God was passive; he waited for commands and only then fulfilled them, while Avraham would search for spiritual opportunities and fulfill them even before receiving an explicit command. Indeed a survey of Noach's and Avraham's life stories reveals this to be the case, and hints that Avraham was the much more impressive person for that reason.
Yet while Noach had to be commanded to build an ark, to enter the ark, to bring animals into the ark, and even to leave the ark - in no place do we find that he was commanded to offer sacrifices upon descending to the newly exposed land. Rather, he noticed that there were more than two of each kosher animal, discovered within himself the desire to thank God for saving him, and put two and two together and decided to offer sacrifices. For once, perhaps for the only time in his life, Noach behaved not like Noach but like Avraham.
It is in reaction to this that God promises never again to destroy the world. The inclination of humanity is evil, but Noach shows that humanity is capable of self-improvement. The spark of initiative and self-improvement which has been lit within Noach will later grow into a flame, enveloping Avraham, then Moshe, and eventually spreading to encompass the entire world as we some day soon enter the messianic era.