Hemodialysis : The blood circulates outside the body of the patient - it goes through a machine that has special filters. The blood comes out of the patient through a catheter (a flexible tube) that is inserted into the vein. The filters do what the kidney's do; they filter out the waste products from the blood. The filtered blood then returns to the patient via another catheter. The patient is, in effect, connected to a kind of artificial kidney.
Peritoneal dialysis : A sterile (dialysate) solution rich in minerals and glucose is run through a tube into the peritoneal cavity, the abdominal body cavity around the intestine, where the peritoneal membrane acts as a semi-permeable membrane.
The abdomen is the area between the chest and hips - it contains the stomach, small intestine, large intestine, liver, gallbladder, pancreas and spleen. Peritoneal dialysis uses the natural filtering ability of the peritoneum - the internal lining of the abdomen. In other words, peritoneal dialysis uses the lining of the abdomen as a filter of waste products from the blood.