The informal term aperiodic tiling loosely refers to both an aperiodic set of tiles, and to the tilings which such sets admit. Properly speaking, aperiodicity is a property of the set of tiles themselves; any given finite tiling is either periodic or non-periodic. Further confusing the matter is that a given aperiodic set of tiles typically admits infinitely many distinct tilings. One proposed formal definition is that a tiling of the plane is aperiodic if and only if it consists of copies of a finite set of tiles, that themselves only admit non-periodic tilings. Link to wikipedia
More
Try google image search with keywords "aperiodic tiling".