What term indicates the swelling of a vein?

The term that indicates the swelling of a vein is varicosity. Varicosity refers specifically to the condition of varicose veins, which are swollen, twisted veins that typically occur in the legs. They result from the failure of the valves in the veins, leading to increased pressure and swelling.

Phlebitis refers to the inflammation of a vein, which may not necessarily involve swelling but does indicate irritation or infection. Thrombosis means the formation of a blood clot within a blood vessel, which can occur in veins but doesn't specifically refer to swelling. An embolism is the obstruction of a blood vessel by an embolus, such as a blood clot, air bubble, or other foreign material, and does not pertain to the swelling of a vein. Thus, varicosity is the most precise term for describing swollen veins.