How do we know The Iliad was improvised orally?
Homer was blind.
This is where poets like Hesiod (from Works and Days, and Theogony) and Homer (Perceived oral poet of the Iliad & Odyssey) used to sing rhapsodies, improvised lyrics with a rhythm, for entertainment at parties or for royalty. They sang of legends of the past and other stories as they came. These improvisations were passed down generation to generation, which are now compiled as Ancient Classics.
I just improvised the answer to this question. Having wasted their time the night before, the girls improvised their presentation today in class. He watched a lot of "Whose Line is it Anyway?" when he was younger. That is why he successfully improvised his lines on the spot. (While the last sentence is slightly redundant, it was given to help illustrate the definition of "improvise" though context clues.)