Why are Mexico, Central America, South America, and the Caribbean called "Latin America"?

Latin America = countries of the Americans where the predominant language and culture descends from those brought from European colonial powers whose language and culture descends from the ancient Roman Empire, where Latin was the official language. These colonial powers were (in chronological order of earliest settlements) Portugal, Spain and france

Other people call all American countries where people speak Spanish, Portuguese, and French Latin America. The words Latin America come from the use of languages that came from Latin. The Spanish, Portuguese, and French languages, spoken by many people in Latin America, are Romance languages.