The Norse peoples were aware of parts of North America, which are referred to as more or less just that; as places or islands. There is nothing indicating they had any conception of it a continent. The places they were aware of are Greenland, Helluland - possibly Baffin Island, Markland - possibly the Labrador coast and Vinland - somewhere around the Gulf of Saint Lawrence, whether Newfoundland, or Nova Scotia or the mainland.

Greenland was colonized in the Viking Age and the colony there declined in the 14th century and was was last heard from in 1410. Konwledge of Greenland and the Inuits were not forgotten. While Columbus was planning to set sail for China in 1492, there was a Native American umiak on display in Oslo cathedral, which'd been taken as a prize in the 14th century. A German traveler to northern Norway in the 15th century also heard stories about the people with 'leather boats' living in the islands to the west.

There's not a lot of textual sources on the Greenland colony, hence we don't even know when it was abandoned. But we have a short reference in a few Icelandic annals mentioning the missionary Bishop Erik Gnupsson departed in 1121 to find Vinland. They do not say why he did so. But the Norse expeditions to Vinland that the Vinland sagas talked about occurred over a century earlier and did not - by the saga accounts nor archaeological evidence - establish or even attempt to establish a permanent settlement. More likely then, he was seeking to find the natives there to convert them. We don't know if he ever found Vinland or even returned, since there's no further record of him after that.

The earliest account of Vinland is from Adam of Bremen who wrote about it around 1070. He'd heard it at the Danish court. Although he does not say much more than it is an island in the west of nice climate where grapes grow, hence the name. (Vín is Old Norse for 'wine' but the language din't really distinguish the plant and its produce; grapes were 'wine-berries'). As a German chronicler of note, Adam of Bremen's account was no doubt the most spread one. But it's about an island, not a continent.

It should probably be said that awareness was not the key to discovery though. Europeans were fully aware of Africa since time immemorial but it still wasn't until the 15th century that the Portuguese started exploring its Atlantic coast.