The cornicle is one of a pair of small upright backward-pointing tubes found on the dorsal side of the last segment of the bodies of aphids. They are sometimes mistaken for cerci

Cercus

Cerci are paired appendages on the rear-most segments of many arthropods, including insects and arachnids but not crustaceans. Cerci often serve as sensory organs, but they may also be used as weapons or copulation aids, or they may simply be vestigial structures.Typical cerci may appear to be...

. They are no more than pores in some species.

These abdominal tubes exude droplets of a quick-hardening defensive fluid containing triacylglycerols called cornicle wax.
There is some confusion in the literature about the function of the cornicle wax secretions. It was common at one time to suggest that the cornicles were the source of the honeydew, and this was even included in the Shorter Oxford English Dictionary

Shorter Oxford English Dictionary

The Shorter Oxford English Dictionary, often abbreviated to SOED, is a scaled-down version of the Oxford English Dictionary . It comprises two volumes rather than the twenty needed for the full second edition of the OED...

and even appears in the 2008 edition of the World Book Encyclopedia

World Book Encyclopedia

The World Book Encyclopedia is an encyclopedia published in the United States. It is self-described as "the number-one selling print encyclopedia in the world." The encyclopedia is designed to cover major areas of knowledge uniformly, but it shows particular strength in scientific, technical, and...

. There also is documentation in the literature for cornicle wax luring predators in some cases.