Born of Erik the Red and Thjodhild (Þióðhildr) in about 970, grandson to Erik's father Thorvaldr (Þorvaldr) Ásvaldsson who'd been exiled from Norway to Iceland, Leif was raised by Tyrke—a thrall of Erik—accepted in time as a hirdman by King Olaf Tryggvason of Norway, and charged later with the mission to bring Christianity to Greenland.
In the year 1000, Leif heard from a merchant Bjarni Herjólfsson about a land farther to the west. Buying Bjarni's boat and gathering a 35-man crew, Leif set sail to find it and landed at what most scholars believe is today's Baffin Island, named in the Icelandic Grænlendinga saga as Helluland (Flat-Rock Land).
Sailing on, Leif came next to what is probably Labrador (named Markland, Forest Land, in the saga), and then two days beyond he reached a place that he named Vinland (Wineland or Pastureland), which is mostly likely Newfoundland, though some scholars speculate that it may have been a location even beyond Newfoundland, perhaps New Brunswick. There Leif Erikson (also spelled Erickson*) and his men wintered before returning to Greenland with grapes and timber, after which Leif settled into the family estate Brattahlid (Brattahlíð) in Greenland and, to the displeasure of his father who remained faithful to the old gods, began preaching Christianity to the Greenlanders.
In the 1960's, archeologists discovered a Viking settlement on the norther tip of Newfoundland, confirming that the Vikings had indeed discovered North America as the sagas told—500 years before Christopher Columbus. While the evidence that this is specifically Vinland is strong, it's open to some dispute; regardless, it is undeniably a Viking settlement. This settlement is called L'Anse aux Meadows today, and it was made a World Heritage Site by UNESCO in 1978.
October the 9th is selected as the date to commemorate Leif Erikson Day because—as explained by President Obama in the 2014 proclamation of Leif Erikson Day:
a group of Norwegian immigrants boarded a ship named Restauration, and with the same sense of hope and determination shared by Erikson and his crew, they crossed the Atlantic in pursuit of the freedoms promised in America. On October 9, 1825, they arrived in New York City, becoming the first organized group of immigrants from Norway to reach the United States.
2014 also marks the 200th anniversary of Norway's constitution.
*Scandinavian names at the time were, and in Iceland still are, patronymic, "-son" or "-dóttir" being added to the father's name (sometimes the mother's name) to indicate "son of " or "daughter of".
(Graphic by Andrew Saur.)