This form of dialysis removes waste products from the blood by passing it out of the body, through a filtering system (dialyser) and returning it, cleaned, to the body.
The waste products pass through the membrane into a dialysis solution (dialysate), then out of the machine. The "clean" blood is carried on through and returned safely to the body.
This happens over and over again throughout the dialysis session. Each time the "clean" blood is returned to the body, it picks up more waste products from the cells it circulates through, and brings these newly-collected toxins back to the dialyser to be removed.
Fresh dialysate is passed through the dialyser continuously, to make the rate of the cleaning process as fast as possible.
As well as cleaning the blood, the dialysis machine also removes excess water. This part of the process is called ultrafiltration which can be done separately without dialysis.
It takes about 4 hours (perhaps more) to complete a good session of haemodialysis, which needs to be done 3 times a week.