America is named for Amerigo Vespucci. Americus is a Latinized version of Amerigo's name, which was the source from which the name America was taken from. Vespucci was the first person to put forth the idea that the land Columbus sailed to was not Asia, but a whole new country in and of itself.
Vespucci made the first trip to the New World in the early 1500s. A map produced by Martin Waldseemuller in 1507 named the new continent America in recognition of Vespucci's theory of this land being a new continent. Vespucci made more than one trip to the New World, discovering that the coast of what would become South America stretched much further south than first believed, lending credibility to the concept that this was a new country.