Often when a muscle is not being used as much it can cause something called fascia to stick to the muscle causing the area to be dehydrated. Fascia is the shiny web-like sheet that goes around muscles as well as all the organs nerves blood vessels and bones. When an area becomes dehydrated, it can become painful, stops the muscles from being able to full length and slows/prevents healing. Kinesiology tape applies a minor tension to the fur/hair follicles pulling it away slightly from the structures underneath to allow water to move back into the area. Since there is more space between the skin and the underneath structures. This works particularly well in horses with oedema.
Kinesiology tape can be used to encourage an animal to use their muscles to be able to strengthen them. Providing that the tape is not applied too regularly, the sensation of the tape will stimulate the sensory nerves in the skin and cause a contraction in the muscle. When this is applied too much the nerves become less sensitive to it resulting in little or no contraction. This can be like when you first put a pair of socks on as initially you will be able to feel that they are on. After a period of time these nerves get used to the sensation and don't feel the need to tell the brain.
Similar to muscle activation, kinesiology tape can provide support by making the animal aware of the area from the feedback given to the nerves. Making an animal aware of an area would ideally make them more cautious and reduce the risk of further injury. This type of tape will also not be as effective if it is used continuously.