Appearing in almost every Final Fantasy game the Genji armor is almost always the most powerful equipment set you can find. It is rare and is usually either stolen from or dropped after defeating a recurring boss/character known as Gilgamesh, a travelling samurai/swordsman who is searching for the ultimate weapon known as Excalibur.
A good example of the Genji's power can be seen Final Fantasy VII: Crisis Core with the armor, which when equipped sets the HP limit to 99,999 and grants auto-Endure and Regen. The Genji shield is incredibly powerful in this game too because it absorbs all elemental attacks and makes Zack immune to all status effects.
Gilgamesh is set to return in some Final Fantasy XV DLC in the near future so it's very possible that he will bring along the Genji Armor he is famed for carrying.