What did Genesis mean to its most ancient audience? What did Genesis tell its ancient readers?

This is a huge question, but I will rely on the work of theologian Walter Brueggemann in his book Genesis: Interpretation: A Bible Commentary for Teaching and Preaching, which focuses on preaching Genesis within a modern context but also provides an account of how ancient Israelite theologians structured Genesis to reflect their own worldview.

Genesis, which was actually one of the later books of the Old Testament to be composed, contains a creation myth that explains the ancient Israelite view of the universe. Unlike other Near East creation narratives, Genesis focused on the idea that creation is good in and of itself. This concept is central to ancient Jewish thought: the material world is not some evil or some illusion that we need to rid ourselves of to attain connection with the godhead, but is a reflection of God and his goodness. Likewise, humans, as part of God's creation, are good. As Brueggemann puts it: "The world has been positively valued by God for itself" (13). Humans, therefore, are to value creation. This differs from, for example, a Platonist notion that sees the world as a shadow of an eternal perfection existing outside of the world.  

Genesis, reflecting ancient Israelite theology, states that God had a will and purpose for creation and that creation only exists for the sake of God's purpose. Creation is of God and for God. The Israelites, says Brueggemann, had a "new thought," a fresh intellectual exercise, that included mythology—a creation story—but still allowed humans a place in shaping the ongoing story of creation. Creator and creation interact. The creator speaks to its creation: "Language is decisive for the being of the world" (18). Further, God's call on creation is a command, but it is also "evocative" rather than "coercive" (18). As we see in the stories told in Genesis, humans can and do deny God's call.

A second important feature of Genesis to ancient Israelites was in its emphasis on covenants. God makes a specific call to Abraham and Sarah in history, wanting them to enter into a community with him and create Israel, a society that is "to fashion an alternative community in [a] creation gone awry" (105). Through his covenant with Israel, God, who is the same God who created the world, will use Israel to redeem the world and bring it back in alignment with his will. God enters into a covenant (mutual obligation) with Abraham and Sarah because they are receptive to his will and his promises (106). They will obey him and he will bless them and their descendants. The ancient Israelites expected to obey but also to be rewarded for their obedience.

In sum, ancient Israelite theologians in Genesis affirmed that God created the world, that material creation was good, that God created the world for a purpose and was involved in his creation through speaking to his creatures, that his creatures were expected but not forced to obey him, and  that God entered into a covenant relationship with Abraham and his descendants so they would be God's chosen people to redeem the world.