In general, a meta material is a material that receives a functional property from the way the materials are structured rather than inherent material properties. That means that the same material structured in different manners can produce a spectrum of properties. There are three general categories for meta-materials, based on what the materials interact with: electro-magnetic, acoustic & mechanical meta-materials. Some systems can produce interesting properties that haven't been seen in nature, including negative refractive index or negative Poisson's ratio.
Origami is a good example of a mechanical meta-material fabrication methodology. Through a series of folds, a flat sheet of paper which is other-wise mechanically isotropic can become anisotropic, having different mechanical stiffness in different directions. It can also be used to create complex geometries from designed repeating folds. This is not because of something inherently special about the paper, it can could also be done other flexible, flat forms like plastic or metal sheets.
I've worked on a variety of meta-material projects. One such project was developing characterization methods for testing paper origami mechanical properties in different directions. Another, scaling and developing an installation based on a negative Poisson's ratio material, using buckling hinges to enable internal reconfiguration upon applied force.