Adidas have recently released a new trainer (shown below) that features a GORE-TEX inner lining. The shoe is the Adidas Moskva (Moscow), a new addition to the City Series. Due to the cold winter climate of Moscow, the GORE-TEX inner lining is a useful new feature: insulating the shoe to keep it warm and also providing waterproofing. Adidas also state that the lining is 'breathable'; which I speculate enables the foot to breath during the summer months when the GORE-TEX is no longer essential for waterproofing and insulation.
GORE-TEX is a trademark of W. L. Gore and Associates, the company developed the GORE-TEX fabric in 1969: the fabric is described as a "waterproof, breathable fabric membrane" that is suitable for all-weather use. GORE-TEX has received three U.S. Patents: which patented the fabric as a "waterproof laminate" and a "porous form of polytetrafluoroethylene". GORE-TEX tends to be used by 'outdoor' sportswear brands like Oakley, Arc'teryx, and The North Face; it is, therefore, somewhat out of the 'norm' for a mainstream sportswear brand, like Adidas, to use the fabric.