Whenever something injected in the body, it leads to inflammation in the area, though, the body reacts by increasing the blood supply and sending more nutrients to the area.
So, the same theory is used in Prolotherapy. Prolotherapy may be defined as, the treatment of soft-tissue damage through the use of injections.
The term prolotherapy is derived from the word prolo, short for proliferation, as the therapy is intended to proliferate tissue growth in the damaged area.

Ligaments are fibrous bands or sheets of connective tissue linking two or more bones. Ligaments can become weak or injured and may not heal back to their original strength or endurance. This is largely because the blood supply to ligaments is limited, and therefore healing is slow and not always complete. To further complicate this, ligaments also have many nerve endings and therefore the person will feel pain at the areas where the ligaments are damaged or loose.
Tendon is a tough yet flexible band of fibrous tissue. The tendon is the structure in your body that connects the muscle to the bones. The skeletal muscles in your body are responsible for moving your bones, thus enabling you to walk, jump, lift, and move in many ways, and in the same manner (as seen in Ligaments) tendons may also become injured, and cause pain.

Prolotherapy uses a dextrose (sugar water) solution, which is injected into the ligament or tendon where it attaches to the bone. Prolotherapy increases blood flow, flow of nutrients and stimulates the tissue, swelling, and pain. The body then launches a course of repair and healing.
This technique is known from more than 2000 years. Hippocrates used it to treat injured shoulders (dislocated, torn shoulder joints) of soldiers. Hippocrates used a hot poker, it would then miraculously heal normally.
George Hackett, often called a pioneer of prolotherapy, was experimenting with and touting the benefits of the procedure. Prolotherapy using injections was derived from a treatment developed by H.I. Biegeleisen called sclerotherapy, used to treat varicose veins.

Difference between sclerotherapy and Prolotherapy

Sclerotherapy is the use of injections of caustics into the veins, in vascular surgery and dermatology, to remove varicose veins and other vascular irregularities. Prolotherapy is the use of injections in the treatment of connective tissue weakness and musculoskeletal pain. Prolotherapy is also called "proliferation therapy" and "regenerative injection therapy."
Prolotherapy treatment is useful for many different types of musculoskeletal pain like, arthritis, back pain, neck pain, fibromyalgia, sports injuries, unresolved whiplash injuries, carpal tunnel syndrome, chronic tendonitis, partially torn tendons, ligaments and cartilage, degenerated or herniated discs, TMJ and sciatica.