The fluidity of a membrane is how stuff or flexible. Butter is a good analogy. Right out of the refrigerator, it's very still. If you leave it on the counter at 25-30 degree C, it gets soft. Heat is more and it melts. It isn't a crystal structure like water/ice, so it transitions between stiff and soft before it totally melts.
The membrane is like this too. Fluidity is important to maintain the function of membrane functions - too stiff or too loose and they won't function properly. When a person inhales an anesthetic (like ether, nitric oxide, or halothane), the small non-polar molecules dissolve in the middle, non-polar part of the membrane. This disrupts the interaction between the fatty acids tails and makes the membrane very loose - disorganized. The membrane proteins in the brain (ion channels) stop working and the brain shuts down. This is how inhalation anesthetics work.
Cells maintain the proper membrane fluidity by using the correct fatty acids in the phospholipids. Longer chains increase fluidity. And cholesterol does both - it increases fluidity at lows temps and decreases fluidity at high temps. It controlled by the cell. Typically, in warm-blooded species, the membrane composition doesn't change much because the temperature is constant. But in ecothermic species, the cell will change the membrane composition to meet the temperature and keep fluidity constant as temperature changes.
Thank you,
Eddie E.