I'm not sure that I would say it "stiffens" membranes, since the presence of cholesterol can actually make membranes less rigid and more fluid. It depends on the rest of the membrane composition. Cholesterol has a very small polar (charged) "head", in relation to the length and width of its uncharged, hydrophobic "tail". The top part of the hydrophobic tail is composed of a rigid series of inflexible rings (the steroid region). So what happens is, the polar head anchors the molecule into one side or the other of the phospholipid bilayer; and the body packs itself between the phospholipids' "tails" on the inside of the layer. Towards the top of the cholesterol molecule the phospholipid tails are forced together more closely in order to make room for the steroid rings. However, towards the center of the bilayer, the cholesterol tail is a standard, relatively thin and fexible hydrocarbon chain -- and it clears more room in the interior of the bilayer for molecules to slide through and move around in, hence an increased degree of fluidity. In general, the more cholesterol there is in a membrane, the less permeable the membrane is to water; the tops of the hydrophobic regions of the membrane molecules are packed far more tightly. I hope that helps with what you're after.