CORDIAL meaning: 1. friendly, but formal and polite: 2. (of a feeling, especially dislike) strongly felt: 3. a…. Learn more. CORDIAL definition: 1. friendly, but formal and polite: 2. (of a feeling, especially dislike) strongly felt: 3. a…. Learn more. The adverb cordially comes from the adjective cordial, which come from the Middle Latin word cordialis meaning "of or for the heart." Something that is done cordially has warmth and friendliness to it, like a host who greets people cordially at a party. Cordially means in a friendly but formal and polite way, or when inviting or agreeing to something. It can also express strong dislike or disapproval. See how to use cordially in sentences and synonyms.