This lattice demonstrates how a solid might contract in the direction perpendicular to the one in which it is being squeezed, rather than expand like a typical solid would.
The Poisson ratio characterizes how much a solid expands in one direction as it is compressed in another. Therefore, a material with a negative Poisson ratio will compress as it is compressed in another. You can imagines squeezing the left- and right-most arms to contract the interior of the lattice shown.
Modeled, rendered, and 3D printed in Autodesk's Fusion 360.