A model conceived by S.J. Singer and Garth Nicolson in 1972 to describe the structural features of biological membranes
Fluid mosaic model is the theorized model of certain biological membranes. One of them is the plasma membrane. Based on this model, the plasma membrane is a lipid bilayer of phospholipids with embedded proteins. It separates the contents of the cell from its outside environment. It is selectively permeable, i.e. some substances may pass through it via passive transport. Other substances would not be able to pass through without using transport mechanisms such as carrier proteins. The plasma membrane regulates what enters and exits the cell and the mechanism is explained through the fluid mosaic model. Accordingly, the plasma membrane is fluid because of its hydrophobic integral components such as lipids and membrane proteins that move laterally or sideways throughout the membrane. That means the membrane is not solid, but more like a ‘fluid‘.
The membrane is depicted as mosaic because like a mosaic that is made up of many different parts the plasma membrane is composed of different kinds of macromolecules, such as integral proteins, peripheral proteins, glycoproteins, phospholipids, glycolipids, and in some cases cholesterol, lipoproteins.
According to the model, the plasma membrane is a lipid bilayer (interspersed with proteins). It is so because of its phospholipid component that can fold in itself creating a double layer – or bilayer – when placed in a polar surrounding, like water. This structural feature of the membrane is essential to its functions, such as cellular transport and cell recognition.
See this Cell biology tutorial for more basic information about the structure of a biological cell