The shrimp vein is the animal's intestinal tract that contains its waste. So, it's not exactly the same as a vein that carries the blood, but because it appears the same way, it's referred to as the vein. Although the idea of eating this is off to many, eating it isn't harmful. It's best to remove it, though. Taking the vein off will give you a tastier shrimp as the vein has a darker taste that is different than the rest.