According to the Random History website, Latin America is named for the Latin language, which is the origin of the languages spoken in that area. The dominant languages in Latin America are Spanish and Portuguese, which descend from Latin.
The Spanish and Portuguese languages came to prominence in Latin America as a result of colonial conquests in the 15th, 16th and 17th centuries. Spanish conquistadors took power in Central America, Peru and Argentina from the Amerindians while the Portuguese established an empire in Brazil. According to Random History, the languages of the colonial powers became the elite tongue in the conquered areas, encouraging more people to speak it as they sought success. As Central and South America were dominated by languages derived from Latin, people began to refer to the area as "Latin America."