They are situated in the posterior parts of the aryepiglottic folds of mucous membrane, and are sometimes fused with the arytenoid cartilages.

[1][2] The word "Corniculate" has a Latin root "cornu".

Cornu means horn like projections.

The projections of Corniculate cartilage look like "horns" hence the name.

[3] This article incorporates text in the public domain from page 1075 of the 20th edition of Gray's Anatomy (1918)