Neath means beneath — under something. You will almost never hear it in ordinary talk. It lives in old poems, songs, and a slightly old-fashioned kind of writing, often spelled 'neath with an apostrophe, as if a piece of beneath had fallen off: 'neath the stars, 'neath the ground. The word you actually want in class, in a shop, or in a message is under or beneath. This sense comes from Old English neoþan, from Proto-Germanic *niþanē, an old 'from below / under' word. There is also a town in Wales called Neath, which is a different word with a different history; this entry is only the under-word.