A thrombosis is the occlusion of a vein by a blood clot. They can happen in any of the body's veins, but tend to be in veins close to the surface, including the veins of the anus. They can be caused by any condition that causes clotting.
A deep vein thrombosis is a thrombosis that occurs in a vein well below the surface of the skin.
Blood flow in veins is generally redundant, so a thrombosis is not usually immediately life threatening. However, they prevent proper blood flow in the affected area and can lead to muscle death if not treated promptly.