It means the foam in the bedding or upholstered furniture has been tested to meet CertiPUR-US rigorous standards for emissions, content, performance, and durability. Specifically, the foam is:

Made without ozone depleters
Made without PBDEs or the following Tris flame retardants: TCEP, TDBPP, TDCPP or TEPA
Made without mercury, lead and heavy metals
Made without formaldehyde
Made without phthalates regulated by the Consumer Product Safety Commission
Low VOC (Volatile Organic Compound) emissions for indoor air quality (less than 0.5 parts per million)