Veins are blood vessels that return blood to the heart. They usually carry deoxygenated blood, except for the pulmonary vein which carries reoxygenated blood back to the heart from the lungs.
Unlike arteries, veins are not under pressure, all of the blood pressure being distributed through the capillaries. Above the heart, blood is returned through veins by the force of gravity. Below the heart, the action of muscles forces blood through the veins as long as the muscles are in motion.
To prevent blood from flowing back through veins, they are equipped with valves that only operate in the direction leading to the heart. If these valves are put under continuous pressure, such as that which occurs when a person stands in place for hours on end (e.g. retail salespersons, doormen), they can break down, leading to the condition known as varicose veins. When a varicose vein develops in the veins around the anus, it's called a hemorrhoid.
Although damage to a vein is serious, it's usually less serious than damage to an artery as pressure on the wound will usually prevent blood from leaking. Moreover, the rest of the body's veins will usually be sufficient to return blood to the heart for redistribution.