What do parents' stories in chapter seven reveal about the villagers' beliefs in Things Fall Apart?

The stories told by the mothers and fathers of Umuofia serve to pass cultural values from parents to children.  However, it is important to note the difference between the stories told by Okonkwo and the stories told by Nwoye's mother.  Okonkwo's stories emphasize masculinity and violence.  These values are present in Igbo culture, but Okonkwo takes these values to the extreme.  Nwoye's mother tells stories such as the story of the turtle, which discourages greed and deception.  This story is similar to stories told in American culture as well.  It resembles Aesop's Fables.  Both sets of stories are told in order to teach children appropriate and acceptable ways to behave in their society.  Nwoye, in particular, misses his mother's stories when he begins to listen to his father's stories in his hut.

In Chapter 7 of Things Fall Apart, what do parents' stories reveal about the villagers' beliefs?

It is evident from the passage that you are refering to that the tribal belief system is one that is not sophisticated scientifically, and still uses parables, fables and myths to explain the world around them. However, it is also clear that these stories have a valuable role in the socialisation of the young, or the way that they learn the received culture of their tribe. Note what we are told about Okonkwo's son and how he regards the stories that his father and mother tell him:

So Okonkwo encouraged the boys to sit with him in his obi, and he told them stories of the land--masculine stories of violence and bloodshed. Nwoye knew that it was right to be masculine and to be violent, but somehow he still preferred the stories that his mother used to tell, and which she no doubt still told to her younger children...

These stories are fables about animals, and seek to explain the natural world in which they live. Thus we can see that both sets of stories have their purpose in terms of socialising the young of this tribe and also indicating the primitive belief system that the tribe have.