Homer and his Iliad and Odyssey are said to be part of an oral tradition. Since the Iliad and Odyssey were written down, it should be emphasized that they came out of the earlier oral period. It is thought that the epics we know today are the result of generations of storytellers (a technical term for them is rhapsodes) passing on the material until finally, somehow, someone wrote it. This is just one of the myriad details we don't know.
An oral tradition is the manner in which information is passed from one generation to the next in the absence of writing or a recording medium. In the days before near-universal literacy, bards would sing or chant their people's stories. They employed various (mnemonic) techniques to aid in their own memory and to help their listeners keep track of the story. This oral tradition was a way to keep the history or culture of the people alive, and since it was a form of story-telling, it was a popular entertainment.
The Grimm Brothers and Milman Parry (1902-1935) are some of the big names in the academic study of the oral tradition. Parry discovered there were formulas (the mnemonic devices) the bards used that allowed them to create part-improvised part-memorized performances. Since Parry died young, his assistant Alfred Lord (1912-1991) carried on his work.