The membrane filters work by the principle of reverse osmosis. Firstly osmosis is the movement of
water from a high concentration to a low concentration, so the the principle of reverse osmosis is the movement of
water from a low concentration to a high concentration.
Firstly the water that is being treated is forced with pressure into a cylinder tube with fibres of semi permeable membrane, so through the principle of reverse osmosis (as the dirty water has a low concentration of water, to the tube with a high concentration of water), the clean water passes through the filter leaving the dirty particles outside of the tube, and so the water is purified.
Here is a diagram I could find on this
http://www.lenntech.com/whatisro.htm