Capillaries are tiny blood vessels that connect arteries and veins, which may be visible on the skin surface, especially where skin is thin, such as the face. Broken capillaries look like thin red threads on the skin that have a webbed appearance, so that they are called spider veins.roken capillaries on your face are more prominent as you age, as your skin usually gets thinner, which makes it easier to see the veins. Excessive alcohol intake. or smoking. Chronic alcohol intake can increase blood pressure, which makes the veins in the face to enlarge.