Homonyms are words that sound the same or are spelled the same but have different meanings. There are three types of homonyms: homographs have the same spelling but different meanings or pronunciations, heteronyms have the same spelling but different pronunciations, and homophones have the same pronunciation but different spellings and meanings. The document provides examples of each type of homonym and additional vocabulary words related to addition, berth, birth, blue, check, and deer.