[sudo-discuss] thermal conductivity question

can someone help me understand the unit W/m.K it's a measurement of thermal conductivity of a material. I don't really understand. I get W/K or K/W but i don't understand where the meter comes in. For a flat material of a specified thickness, i would understand watts per degree per square meter, but i don't get the single meter thing. here is an example: http://www.sciencedirect.com/science/article/pii/S001122759700146X how does that measurement work?