While he was a very underrated explorer and isn't remembered as much for his voyages, his biggest accomplishment is a pretty good one.
Columbus and other explorers thought they had discovered a quicker way to Asia by traveling west instead of east. In fact, Columbus still believed that when he died.
Vespucci was the one who recognized the lands were not Asia but an entirely new continent. He was fascinated with the tales of Marco Polo and had a good idea of the geography of Asia because of the books.
However, when he was sailing around Rio de Janeiro and the rivers there, he began to suspect this land didn't match what he knew to be true about Asia. The coastlines, the constellations, the distance of time travelled... none of it made sense.
He was smart enough to realize this was an entirely new continent. He wrote back with his suspicions, and soon his beliefs came to be accepted everywhere.
The not quite realistic map to the left form 1507 shows a version of his name. "America" is close to "Amerigo", and from this point on the New World became known as America.
His biggest contribution: recognizing the land was new and lending his name to it.
Vespucci's business helped outfit one of Columbus's journeys.
He met and talk with Christopher Columbus
He sailed for both Spain and Portugal, even though he was actually from Italy!