The National Heart, Lung, and Blood Institute lists high blood pressure, malnutrition, aging and vascular illnesses as potential causes for a vein in the hands bursting. One of the common vascular issues is a clot formation in one of the blood vessels.
NHLBI further explains that if a clot forms, the flow of blood through the affected vessel is slowed or stopped altogether. The blood builds up behind the clot, causing the vein to bulge. The pressure of the additional blood can cause the vein to burst and blood to leak out under the skin.
Nutra Legacy states that the main symptom of a burst vein is a change in the appearance of the skin on the affected hand. The skin around the affected area becomes red, resembling a fresh dark bruise. Healing can be aided by raising the affected hand above the heart and applying pressure to the area until the bleeding stops.