Deveined shrimp refers to shrimp that have had their digestive tract removed. The "black vein" in a shrimp is actually its digestive tract, which can contain sand, grit, and sometimes, dark matter that some people find unappetizing. While not harmful to consume, many people prefer to remove the vein for aesthetic and taste reasons. To devein shrimp, you make a shallow cut along the back of the shrimp and remove the black or dark-colored vein that runs along the length of the body. This can be done using a small paring knife or a special shrimp deveining tool.