Taurine is an essential amino acid for the cat, which means that the cat can not synthesize sufficient Taurine from other amino acids. Humans and dogs, for example, synthesize Taurine from the amino acids Methionine and Cystine.

Preformed Taurine is only available from animal tissue, and high concentrations of Taurine are found in the heart muscle, skeletal muscles, brain and eyes of mammals, as well as the meat from clams and oysters.

Taurine is very sensitive to heat, and Taurine content in meat is greatly reduced after cooking.
For example:

A deficiency of Taurine in cats will cause Central Retinal Degeneration (eye lesions) resulting in total blindness within two years if the deficiency is not remedied, Dilated Cardiomyopathy (enlargement of the heart's chambers resulting in thinner, weaker heart walls) and reduced reproduction in queens and growths in kittens.

The National Research Council suggests in its literature a requirement of 400 mg of Taurine/kg of diet for growing kittens and for the maintenance of adult cats, and a minimum of 500 mg of Taurine/kg of diet for reproducing cats. The American Association of Feed Control Officials (AAFCO) outlines in its Nutrient Requirements for Cats a minimum of 0.20% Taurine in the diet for growth, reproduction and adult maintenance.
The Cornell Book of Cats by the Cornell University describes that "The AAFCO Nutrient Profiles for Cat Foods requires that canned foods contain a minimum of 2000 milligrams taurine per kilogram of diet; ..."

The role of Taurine in the body is complex. It is a building block of all the other amino acids as well as a key component of bile, which in turn is needed for the digestion of fats and absorption of fat-soluble vitamins. It is vital for the proper utilization of Sodium, Potassium, Calcium, and Magnesium, and prevents loss of Potassium from the heart muscle. Also, Taurine has a protective effect on the brain and is essential in maintaining eye function.

When buying Taurine supplements to be used in home preparing cat food, most Taurine supplements are labelled "L-Taurine". However, there is no difference between Taurine and L-Taurine.
The "L" of L-Taurine stands for "levo" which means that, the groups at the lowest numbered asymmetric carbon atom are placed at the left - a description of the configuration of the molecular structure of Taurine. In other words: all Taurine is L-Taurine - the "L" is simply bonus information.

Today, Taurine supplements are usually the result of synthesis by Sodium Sulfite sulfonation of Ethylene Chloride followed by ammonolysis with anhydrous NH₃ (Ammonia without water) or with aqueous NH₃ (Ammonia with water) and Ammonium Carbonate.
However, references from 1901 and 1918 point out that it can also be isolated from ox bile or from the large muscle of abalone.

Synthesized Taurine has the same molecular structure as Taurine found in animal tissue, and is absorbed by an organism (your cat) in the same way as naturally occurring Taurine.

The Merck Index 9043, page 1433

The Merck Veterinary Manual 8th Edition
Table 48 AAFCO Nutrient Requirements for Cats, page 1627

Nutrient Requirements of Cats Revised Edition by the National Research Council, page 13

The Cornell Book of Cats 2nd Edition
by the Faculty, Staff, and Associates Cornell Feline Health Center, page 78 and page 211

Prescription for Nutritional Healing 2nd Edition by James F. Balch, M.D. and Phyllis A. Balch, C.N.C. page 41