Norse points backward in time. It describes the people of early Scandinavia and everything that came from them: their language, their gods, their ships, their legends. The words you meet it in most are Norse mythology, Norse gods and Norse legends. For people in Scandinavia today, English usually reaches for Norwegian, Swedish, Danish or Scandinavian instead, and keeps Norse for the old world. It also has a narrower use meaning simply 'of Norway', so the boundary is not perfectly fixed. It is always written with a capital N.

As a noun, Norse is the language itself, not the people. In careful writing the full name is Old Norse, and the packet's source treats plain Norse as a synonym of it. It belongs to the North Germanic family, the branch that also holds the modern Scandinavian languages. You meet the word in history, in language study, and beside old poems and sagas, so it carries a formal, written feel. Like other language names it takes no article: written in Norse, not written in the Norse.