The lipid composition of a membrane contributes to its overall properties. This allows a cell to control how its membrane interacts with the environment, including its shape and permeability.
Lipids form a bilayer in an aqueous environment, as they are amphipathic molecules. This is due to them having a hydrophilic head group, which faces outwards, and hydrophobic tails, which face the middle of the membrane. Although other structures are able to form from lipids, such as micelles and liposomes, only bilayers form in cells.
Proteins are able to insert into the bilayer, to produce a fluid mosaic structure. This model (fluid mosaic) states that the membrane is highly fluidic, allowing lateral movement. Studying membranes with fluorescence-recovery after photobleaching (Frap) allows the lateral movement to be observed, identifying immobile proteins. There are issues with the fluid mosaic model, however - complete recovery is never observed. This is, in part, due to membrane rafts (which are less mobile and more rigid).