Natural gut strings are made from the intestines of a number of large animals, most commonly the cow and the sheep. Depending on what properties are required of the string, raw material may be taken from a number of places in the intestine, because the collagen in the intestine has varying amounts of orientation from layer to layer. It is more randomly oriented in the mucosa, which is more stretchy and has a lower tensile strength, than it is in the mucosa. Natural gut strings may even be made from threads of collagen harvested from different parts of the intestine.
(taken from http://www.uoguelph.ca/zoology/devobio/210labs/endol.html)
Figure 1. A cross-section of the intestinal tract.
After the appropriate part of the intestine has been harvested, it is treated with various solvents in a water-based process to remove all components except for the collagen. The collagen threads are then bundled and twisted together, and dried under tension for several days. 
Natural gut strings are praised for their "liveliness," and their insurpassable "feel." What is it about gut strings that give them so much "bounce"?
Collagen is a major fibrous component of many types of connective tissue. There are at least 16 known types of collagen, which form varying structures, but have the same purpose -- to provide strength and resilience to tissue, and to help tissue stretch. All collagens have a right-handed triple helix structure, and the difference in each arise from the segments that interrupt the helix and cause them to fold into other kinds of structures.
The fundamental structural unit, the right-handed triple helix, consists of three coiled subunits, chains that are wound around each other. These chains are unusually rich in glycine, proline, and hydroxyproline, which allow them to form the triple helix -- the side chain of glycine (an H atom) is the only one small enough to fit into the center of a three-stranded helix. The rigid triple helix geometry is fixed by the angle of the C-N bond of peptidyl-proline or peptidyl-hydroxyproline. The chains subunits are held together by hydrogen bonds that link the peptide amine bonds of glycine residues to peptide carbonyl groups in an adjacent polypeptide. The triple helix of collagen is 300 nm long, and only 1.5 nm wide.
Collagen fibrils are formed by the packing together of many three-stranded collagen molecules. Fibrils have a diameter of 50-200 nm, depending on the collagen type. The ends of adjacent collagen molecules are displaced from one another by a distance 67 nm, which produces the striated appearance seen in electron micrographs, with bands spaced about 67 nm apart. The packing of collagen molecules is stabilized by covalent aldol cross-links between lysine or hydroxylysine residues at the C-terminus of one collagen molecule and the N-terminus of an adjacent one.
Figure 1. The structure of collagen on several length scales. (a-c) The three subunits of collagen coil together into a triple helix, with the H side group of glycine fitting into the center of the molecule. Each subunit contains 1050 amino acids, and when wound the helix is about 300 nm long. (d-e) In a collagen fibril, adjacent collagen molecules are staggered with their ends 67 nm apart, producing visible striations in stained collagen.
(taken from Lucis, at http://www.imagecontent.com/Lucis/applications/bio/tem1/side/tem1-side.html)
Figure 2. An electron micrograph of collagen fibrils.
In tendons, these fibrils are then packed side-by-side in parallel bundles called collagen fibers, which have high tensile strength and must withstand large forces. Even in cartilage, however, where collagen fibrils are randomly oriented, the rigidity of the macromolecules give strength and compressibility to the cartilage matrix, allowing it to absorb shocks on joints.
(taken from http://ttb.eng.wayne.edu/~grimm/ME518/Images)
Figure 3. Collagen fibrils arranged into fibers.
Due to collagen's structure, several tissues in the body, such as skin, are capapble elastic deformation under a large amount of strain. It is designed for stretching -- how would we benefit from tendon or cartilage that could not regain its original shape after a strenuous event?
The amount of strain that a tissue with a collagen matrix can easily undergo depends on the amount and orientation of the collagen within the tissue. The protein's high amount of order on the secondary and tertiary levels contribute to its strength as well; in fact, collagen is stronger per unit weight than steel.
At low strain, collagen fibrils and fibers uncrimp, and as strain increases, collagen begins to carry load. At higher strain, molecular stretching and slipping of fibrils and fibers occurs. This viscous sliding of the collagen fibrils, which align in the force direction, dissipates the load applied. As collagen is strained beyond its yield point, the crosslinks between fibrils break and defibrillation and eventually failure occurs.
The mechanical properties of fibrous collagen networks with low levels of crosslinking between fibrils are dominated by the viscous sliding of collagen molecules and fibrils. At higher levels of crosslinking, the fibrillar units are more stabilized, and the mechanical properties are dominated by elastic stretching of the nonhelical ends, the crosslinks, and the triple helix. 
The collagen molecule contains both rigid and flexible regions, and these may serve different purposes when the molecule is strained. It is thought that the more rigid sections transfer stress throughout the molecule, while the more flexible sections store elastic energy. The storage and dissipation of energy applied at joints is precisely what tendons and ligaments, which contain collagen, are meant to do. The observed elastic spring constant for collagen in humans is 3.7-4.0 GPa , but this value will change significantly with various factors, such as age (of the body the collagen was harvested from), and pH.
Because collagen is a biological material, it is not surprising that its elastic modulus is dependent on pH. If the pH of the surrounding solution is too acidic or too basic, collagen's elastic modulus decreases. Specifically, Silver et al. found that for pHs approaching the pKa of carboxylic acid (3.5) or amine (10.6), the elastic modulus of collagen begins to decrease.  It is hypothesized that the charged pairs on the outside of the triple helix stabilize the molecule, and that the mechanism of elastic energy storage is related to the separation of the charged pairs. For a pH within the range of 3.5 to 10.6, the amine groups of collagen will be protonated and the carboxylic acids will not, maximizing the charge-charge interactions on the surface of the triple helix.
(taken from Silver FH et al., J Appl Polymer Science 86: 1984, 2002)
Figure 4. Proposed mechanism for elastic energy storage in collagen. Flexible regions, represented as springs, resist elongation because of charged pairs, which also help them regain their original length.
 Pacific Natural Gut Strings, http://www.pacificstrings.com
 Lodish et al., Molecular Cell Biology, 4th edition, 2000, 979-984.
 Silver FH et al., Transition from Viscous to Elastic-Based Dependency of Mechanical Properties of Self-Assembled Type I Collagen Fibers, J Applied Polymer Science 79: 134-142, 2001.
 Silver FH et al., Viscoelastic Properties of Young and Old Human Dermis: A Proposed Molecular Mechanism for Elastic Energy Storage in Collagen and Elastin, J Applied Polymer Science 86: 1978-1985, 2002.