I was introduced to it 4 years ago, by a Japanese sports massage therapist and I call it magic tape.
Something hurts and you put some kinesio tape on it and viola!..it stops hurting. Pure magic.
I understand (roughly) the science behind it, but there's no way it should work as well as it does.
What kinesio tape actually is, is a very strong, very smooth tape with a nifty heat-activated glue - i.e. support strapping that takes up the smallest amount of skin space possible and adds only very small bulk.
Kinesio tape is not a support tape. You use it quite differently than you would with a standard elastic support tape. I have other EST that is much stronger than kinesio tape, that I use when I need support.
It's put on with very little tension, usually along the direction of the muscle/tendon. I think the small level of relaxation in the skin encourages whatever is underneath to relax, allowing more blood, promoting quicker healing.
No, it won't 'fix' issues, but it's amazing for low/medium level pain and that alone can be enough to push your body on the right track for recovery.