Plato referred to Homer as "the teacher of Greece." This was actually not intended as a compliment. Plato was suggesting that because the Homeric poems were widely used as school texts, and because they were so ubiquitous in Greek cultural life, that people absorbed many false beliefs from them, including, worst of all, stories about the gods behaving immorally.
Many teachers in antiquity tried to redeem Homer from philosophical critique by allegorizing some of the stories (especially the sexual adventures of Odysseus) and drawing moral lessons from the poem.
The first lesson Greeks would learn from Homer is that the gods intervene frequently in human lives. One should obey divine laws because the gods are always watching, sometimes even moving around in the human world in disguise. The gods are sometimes presented as agents of wisdom and rectitude and at other times as powerful and capricious personalities, but they are always to be feared and obeyed.
Next, the law of hospitality is very important in The Odyssey. People who violate their obligations to hospitality, such as Polyphemus (a bad host) or the suitors (bad guests) will eventually be punished by Zeus, who is the patron god of guest and strangers.
Finally, leadership is shown to carry with it great responsibility. A good leader is never a tyrant; rather, he is wise and dedicated to the good of his followers.
For modern readers, Homer reveals the culture and ideas of sub-Mycenaean and archaic Greece and also is an important example of oral-derived literature. It shows many of the typical compositional and ideological characteristics of oral traditional society.