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It is the process in which an artificial kidney/dialyser is used to filter the blood of a person whose kidneys are damaged.
In this process, blood is taken out from the main artery, mixed with an anticoagulant, such as heparin and then pumped into the apparatus called dialyser.
In this apparatus, blood flows through channels or tubes made of cellophane. The membrane is impermeable to macromolecules such as plasma proteins but permeable to small solutes such as urea, uric acid, creatinine and mineral ions.
The membrane separates the blood flowing inside the tube and the dialyzing fluid(dialysate), which has the same composition as that of plasma, except the nitrogenous wastes. 
The cellophane membrane allows the passage of molecules based on concentration gradient. As nitrogenous wastes are absent in the dialyzing fluid, these substances from the blood freely move out, there by clearing the blood of its wastes. This process is called Dialysis.
The cleared blood is pumped back to the body through a vein after adding anti-heparin to it. Each dialysis session lasts 2 to 6 hours. 
This method is a boon for thousands of uremic / kidney failure patients all over the world!
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Dialysis is a process removing waste and unwanted water from blood . in the body it is done by kidneys naturally