The word Wagyu refers to all Japanese beef cattle ('Wa' means Japanese or japanese-style and 'gyu' means cattle).

Wagyu beef is highly marbled, meaning that the muscle is finely interspersed with monounsaturated fat. This marbling gives the beef its “melt in the mouth” moisture and tenderness. When cooked, the marbling is absorbed into the muscle and gives the meat its tenderness and flavour. 

The most exclusive Wagyu in the world comes from Kobe, Japan.  People use the terms Kobe and Wagyu beef interchangeably in the U.S. thinking it refers to the same premium imported Japanese beef, when it does not.  Under Japanese law, Kobe beef can only came from Hyōgo prefecture (of which Kobe is the capital city) of Japan.