Cory is taken from the root word for heart in Latin "cor": the Medieval Latin word cor (heart; mind, soul) which was derived from the Proto-Indo-European root "kerd-". This Latin word is the one which gave the Romance languages their words for heart: French - coeur; Spanish - corazón; Portuguese - coração; Italian - cuore; Provençal - cor. So, the English meaning for Cory is heart, tender hearted, brave hearted.
The name Cory started as an Irish surname. It is derived from the Greek "corys", meaning "Helmet". It also means "The Chosen one" in Germanic languages.