We know what we know about Eric the Red and his son Lief Ericson because their stories were written down in a saga.
The Saga of Eric the Red tells us that Eric's father was Thorvald Asvaldson, and that thus his real name using his patronym is Eric Thorvaldson. Thorvald was exiled from Norway after killing several men, and took his family, including Eric, to Iceland. When Eric grew up he was known for his red hair and his fiery temper, and thus earned the name Eric the Red. Like his father he also killed several men in personal disputes, one regarding the death of some of his slaves (thralls), and another regarding some borrowed boards or wood working tools. Following these killings he was exiled from Iceland for three years by the Althing.
Being popular enough to convince a party to accompany him he set off for lands other Vikings had sighted briefly to the west when lost in a storm. He lived and explored in Greenland for the full three years of his banishment from Iceland. Having found the fjords of the island of Greenland habitable by Norwegian standards he returned to Iceland, and convinced 25 ships to accompany him on a mission to colonize this new land. Some turned back and others were lost at sea, but Eric arrived in Greenland with about 16 ships, and around 500 settlers. The colony prospered, and Eric became a rich leader. If you consider Greenland a part of the N. American continent, then you can make a good case for Eric as the discoverer of America.
Eric’s son Lief grew to be a strong leader, and an explorer himself. He sailed west and found rich lands there which he named Vinland, but soon after he returned to Greenland the island was stricken with a plague brought from Iceland, and many of its inhabitants, including Eric the Red, died. Lief was forced to take his father’s place as chieftan, and stay in Greenland nursing the colony back to health. At one point Greenland may have reached around 3000-4000 inhabitants, but the dreams of settling further west came to little as the Greenlanders struggled to survive in their harsh environment which modern scientists tell us became harsher with a cooling cycle. Several hundred years after Eric and Lief the Greenlanders were cut off from Europe, and the colder climate brought the Innuit peoples south, and into conflict with the Vikings that survived in the bleak conditions. Around a hundred years before Columbus “discovered America” the colony in Greenland ceased to be able to sustain itself. No one knows if there were any survivors where they went, but Champlain’s stories of “Indians” with fair skin and hair do not sound as outlandish from a hundred years out, as they do from Lief Erickson’s time 400 years earlier. The sagas don’t tell us much about these later years, so all we can do is speculate, wonder, and hope for new evidence from archeologists or historians.