In Chinua Achebe's, Things Fall Apart what does this proverb mean: "When mother cow is chewing grass its young ones watch its mouth."
Young ones learn by watching their elders.
A child learns by what he sees his parents do, not by what he hears his parents say.
There are many African proverbs in Things Fall Apart, by Chinua Achebe. He writes of a culture that is steeped in tradition and one that places great importance on fairness. There is no king, but a rudimentary form of democracy.
You will note that many of the proverbs concern animals. Animals are an important part of the Igbo culture, as with other primitive cultures, and often the people use animal metaphors such as this to teach various truths and lessons of their culture.