This blood dialysis is also known as hemodialysis.
It is the process of purification of blood of a person who is suffering from renal failure.
In the process of hemodialysis, smaller molecules like urea and other metabolic wastes are separated from the blood; while larger molecules like proteins are retained in the plasma.
In the dialyzing machine blood flows through long semipermeable membrane tubes. These tubes are present in a tank containing a special fluid called dialysate or dialyzing fluid.
Dialysate is isotonic to blood but do not contain nitrogenous wastes like urea etc.
Blood from radial vein of hand is passed through dialyzing machine containing dialysate. During dialysis, waste products from blood diffuse into the dialysis fluid.
This makes blood clear of considerable amount of nitrogenous and other waste products.