Honeydew is a food source that resembles a sugary, honey-like liquid, which can serve as a Food source. Honeydew can only be generated by an Aphid. Additionally, Honeydew cannot be generated Underground.
Honeydew generally isn't that important to the survival of the colony. It can still feed Ants however, so if you have an Aphid nearby, you can sacrifice Honeydew instead of Meat or Green Food. Honeydew is also very useful as a quick food source to get high stocks of food during Autumn, before Hibernation starts.