Deveining is the process of removing the long black strip ("vein") along the back of a shrimp before cooking it. It's not actually the shrimp's vein you're removing (even though we call it that). It's the digestive tract. I don't know which is less appealing, vein or digestive tract, but we're removing it either way. I always buy my shrimp already peeled and deveined, so I don't have to mess with it. It makes it much easier to prepare shrimp whenever the craving hits.