A semipermeable membrane is a membrane which will allow certain molecules or ions to pass through it by diffusion (sometimes "facilitated diffusion"). The rate of passage depends on the pressure, concentration and temperature of the molecules (or "solutes") on either side, as well as the permeability of the membrane to each solute.
Depending on the membrane and the solute, permeability may depend on solute size, solubility properties, or chemistry. An example of a semi-permeable membrane is a lipid bilayer, on which is based the plasma membrane that surrounds all biological cells. Many natural and synthetic materials thicker than a membrane are also semipermeable.