Artery: A vessel that carries blood high in oxygen content away from the heart to the farthest reaches of the body. Since blood in arteries is usually full of oxygen, the hemoglobin in the red blood cells is oxygenated. The resultant form of hemoglobin (oxyhemoglobin) is what makes arterial blood look bright red.
Arteries are part of the efferent wing of the circulatory system. ("Efferent" from the Latin "ex", out + "ferre", to bear = to bear out or carry away. What the arteries are carrying away is blood from the heart.)
By contrast, a vein is a blood vessel that carries blood low in oxygen content from the body back to the heart. The deoxygenated form of hemoglobin (deoxyhemoglobin) in venous blood makes it appear dark. Veins are part of the afferent wing of the circulatory system which returns blood to the heart.