In biology, the membrane fluidity refers to the viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 of the lipid bilayer

Lipid bilayer

The lipid bilayer is a thin membrane made of two layers of lipid molecules. These membranes are flat sheets that form a continuous barrier around cells. The cell membrane of almost all living organisms and many viruses are made of a lipid bilayer, as are the membranes surrounding the cell nucleus...

 of a cell membrane

Cell membrane

The cell membrane or plasma membrane is a biological membrane that separates the interior of all cells from the outside environment. The cell membrane is selectively permeable to ions and organic molecules and controls the movement of substances in and out of cells. It basically protects the cell...

.
The membrane phospholipid

Phospholipid

Phospholipids are a class of lipids that are a major component of all cell membranes as they can form lipid bilayers. Most phospholipids contain a diglyceride, a phosphate group, and a simple organic molecule such as choline; one exception to this rule is sphingomyelin, which is derived from...

s incorporate fatty acid

Fatty acid

In chemistry, especially biochemistry, a fatty acid is a carboxylic acid with a long unbranched aliphatic tail , which is either saturated or unsaturated. Most naturally occurring fatty acids have a chain of an even number of carbon atoms, from 4 to 28. Fatty acids are usually derived from...

s of varying length and saturation

Saturation (chemistry)

In chemistry, saturation has six different meanings, all based on reaching a maximum capacity...

. Shorter-chain fatty acids, and ones with greater unsaturation, are less stiff, less viscous and have lower melting points.
Changes in membrane-dependent functions, such as phagocytosis and cell signalling, are hypothesized to depend upon the cell-membrane fluidity.
This hypothesis lost favor, but has re-emerged recently with the discovery of discrete lipid domains, dubbed 'lipid rafts' in cellular membranes
The hypothesis is still controversial.