If something is paper-thin, it is extremely thin — as thin as a sheet of paper, or close to that. You can say it of walls, ice, fabric, or a slice of meat. People also stretch it: a paper-thin lead in a game, a paper-thin excuse, meaning the gap or the reason is so slight it might as well be nothing. It sounds a little vivid and informal; in a science class you would more likely say very thin, or give a number. Though actually it does not mean made of paper. A paper-thin wall is still a wall. Before a noun, English often keeps the hyphen: paper-thin walls.