Deep vein thrombosis (DVT) is a condition wherein a blood clot develops in one of our "deep" veins, blocking the venous blood flow. Pieces of this blood clot may break off, travel with the blood stream and get lodged in the lung circulation. This is called pulmonary embolism and can be a life threatening condition. DVTs can occur anywhere in the body, but are most frequently found in the deep veins of the legs, thighs and pelvis.
Thrombophlebitis is a condition in which there is both inflammation and a blood clot in a vein, more typical in superficial veins (superficial thrombophlebitis).
Veins should not be confused with arteries. The arterial system directs blood flow (rich in oxygen) from the heart to the body, while the venous system returns blood (poor in oxygen as it has been consumed) back to the heart. Have you noticed that medical illustrations indicate the blood vessels red and/or blue? The red blood vessels represent the arteries; the blue ones represent the veins. This simulates reality as indeed high oxygen levels in the arterial blood give it a bright red color, while low oxygen levels in the venous blood make it look dark blue.
Another major difference of the veins compared to the arteries is that veins have one-way valves. Arteries do not need valves as the blood flow is maintained by the pressure generated by the heart pumping. Blood pressure in the veins is lower than that of the arteries and valves facilitate blood flow (e.g. maintaining flow "upwards" against the gravity). When the leg muscles contract they squeeze the deep veins and the valves open.
Our extremities (arms and legs) have two distinct systems of veins: superficial and deep. The superficial system is made up of veins that are close to the skin. These are the blood vessels you frequently can see on your hand arms, or legs that can become more prominent when you exercise. The deep system is comprised of larger veins deep within the muscles of the extremities. The two systems are connected by small communicating (perforator) veins. All veins eventually merge to form the big central veins in the abdomen and chest. Venous return to the heart occurs predominately through the deep veins, that is why a deep venous clot (thrombosis) has significantly more adverse sequelae than a superficial venous thrombosis.