Speaking in literal terms, the word Wagyu means Japanese Cow.
Wagyu Beef is known for it's Marbling. Marbling is the intramuscular fat found dispersed in-between the muscle layers, where as your other cattle breeds only have a fat layer on the edge of each cut. The fat in other cattle is saturated, which is not so good for your health.
It's all about the intense fat marbling in the meat, it is what gives it the rich flavor. A good quality, high grade cut of Wagyu will literally melt in your mouth.
Wagyu on the other hand is naturally predisposed with a gene to convert saturated fat into unsaturated fat.