Nigh is an old-fashioned word that can be used as an adjective or adverb to mean near or nearly. Something that is nigh impossible — like knitting a sweater in one night — will be very difficult to accomplish.
As an adjective, nigh is an older form of the word "near," both of which are rooted in the Old English word neah. People like to use the word nigh when they talk about the apocalypse: "Repent! The end is nigh." It's most common to use nigh today when you're trying to sound poetic or referencing the archaic or biblical uses of the word.