Kinesiology tape is a stretchy tape applied to the skin used to decrease pain and promote blood flow to the region. 

Kinesiology tape stimulates receptors in the skin which helps to decrease pain in the area, similar to rubbing on your elbow if you hit it on a table. The tape also lifts the skin away from the muscles and fascia which promotes blood to the area to accelerate the healing process. Unlike traditional athletic tape, kinesiology tape is stretchy so that it promotes movement instead of restricting it. 

Kinesiology Tape Research

When applied to a young, active patient population with a clinical diagnosis of rotator cuff tendonitis/impingement, kinesiotape may assist clinicians to obtain immediate improvement in pain-free shoulder abduction range of motion
— Journal of Orthopedic and Sports Physical Therapy
This review highlights that kinesiology tape is superior to minimal intervention for pain relief. Existing evidence does not establish superiority of kinesiology tape in reducing disability when compared to either minimal or other forms of intervention. Taken together, our review indicates that kinesiology tape, when used in combination with conventional therapy, may be effective in reducing pain
— British Journal of Sports Medicine
These results demonstrated that kinesiology tape application with proper tension to the quadriceps effectively attenuates various types of pain and improves active range of motion and proprioception in osteoarthritis patients. Thus, kinesiology tape may be a suitable intervention to improve pain, active range of motion, and proprioception in patients with osteoarthritis in clinics.
— American Journal of Physical Medicine and Rehabilitation