(1) Feeding on both animals and plants. (2) Intensely interested in everything.
Example:
Good writers are often also omnivorous readers who enjoy equally fiction and nonfiction, prose and poetry, philosophy and science.
We tend to think of human beings as omnivorous, but in fact there are many kinds of plants that we simply cannot digest. Bears are truer omnivores. Their diet can include bulbs, berries, nuts, young plant shoots, insects, grubs, and dead animals, including fish, deer, and beaver. Humans do seem to possess an omnivorous curiosity. And it probably took that kind of curiosity -- plus a good deal of courage -- to be the first human to eat an oyster.