Flying Food is a recurring joke within the Heathcliff comic strip. Its punchlines and themes are notably similar to another recurring joke, Fish Food.Edit
In comics containing Flying Food, Heathcliff's lunch will generally sprout wings and fly away from him, even if his lunch is something that as a rule does not have wings, such as a sandwich or a box.
The Flying Food is, presumably, a nod to the habit of real-world cats chasing birds and other avian creatures. As Heathcliff is a cartoon cat who often eats more human food, much humor is derived from this regular food, such as pizza, flying away with wings. There may also be the implication that, because Heathcliff is a cat, his food is composed of living birds.