[sudo-discuss] thermal conductivity question

[Jake]

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?